diff --git a/README.md b/README.md
index dbf4b9e7..db5f9f30 100644
--- a/README.md
+++ b/README.md
@@ -71,15 +71,15 @@ Example 1: Fill a 1d-histogram in C++
         auto h = bh::make_static_histogram(bh::regular_axis(10, -1.0, 2.0, "x"));
 
         // fill histogram with data
-        h.fill(-1.5); // put in underflow bin
-        h.fill(-1.0); // included in first bin, bin interval is semi-open
-        h.fill(-0.5);
-        h.fill(1.1);
-        h.fill(0.3);
-        h.fill(1.7);
-        h.fill(2.0);  // put in overflow bin, bin interval is semi-open
-        h.fill(20.0); // put in overflow bin
-        h.wfill(0.1, 5.0); // fill with a weighted entry, weight is 5.0
+        h.increment(-1.5); // put in underflow bin
+        h.increment(-1.0); // included in first bin, bin interval is semi-open
+        h.increment(-0.5);
+        h.increment(1.1);
+        h.increment(0.3);
+        h.increment(1.7);
+        h.increment(2.0);  // put in overflow bin, bin interval is semi-open
+        h.increment(20.0); // put in overflow bin
+        h.wincrement(0.1, 5.0); // fill with a weighted entry, weight is 5.0
 
         // access histogram counts, loop includes under- and overflow bin
         const auto& a = h.axis<0>();
@@ -132,7 +132,7 @@ Example 2: Fill a 2d-histogram in Python with data in Numpy arrays
     rphi[:, 1] = np.arctan2(y, x)         # compute phi
 
     # fill histogram with numpy array
-    h.fill(rphi)
+    h.increment(rphi)
 
     # access histogram counts (no copy)
     count_matrix = np.asarray(h)
diff --git a/doc/rationale.qbk b/doc/rationale.qbk
index 3e9c5c04..96e5a07b 100644
--- a/doc/rationale.qbk
+++ b/doc/rationale.qbk
@@ -21,7 +21,7 @@ Properties
     Getter/setter-like functions are wrapped as properties.
 
 Keyword-based parameters
-    C++ member functions :cpp:func:`histogram::fill` and :cpp:func:`histogram::wfill` are wrapped by the single Python member function :py:func:`histogram.fill` with an optional keyword parameter `w` to pass a weight.
+    C++ member functions :cpp:func:`histogram::fill` and :cpp:func:`histogram::wfill` are wrapped by the single Python member function :py:func:`histogram.increment` with an optional keyword parameter `w` to pass a weight.
 
 [endsect]
 
diff --git a/doc/tutorial.qbk b/doc/tutorial.qbk
index e51119ee..c3eba018 100644
--- a/doc/tutorial.qbk
+++ b/doc/tutorial.qbk
@@ -26,14 +26,14 @@ How to make a 1d-histogram in C++ and to fill it:
          * axis are placed in the overflow and underflow bins.
          * Normally you would loop over a source of values.
          */
-        h.fill(-1.5); // put in underflow bin
-        h.fill(-0.5);
-        h.fill(1.1);
-        h.fill(-1.0); // included, interval is semi-open
-        h.fill(0.3);
-        h.fill(1.7);
-        h.fill(2.0);  // put in overflow bin, interval is semi-open
-        h.fill(20.0); // put in overflow bin
+        h.increment(-1.5); // put in underflow bin
+        h.increment(-0.5);
+        h.increment(1.1);
+        h.increment(-1.0); // included, interval is semi-open
+        h.increment(0.3);
+        h.increment(1.7);
+        h.increment(2.0);  // put in overflow bin, interval is semi-open
+        h.increment(20.0); // put in overflow bin
 
         /* Fill histogram with a weighted count. This increases the
          * bin counter not by one, but by the specified weight.
@@ -46,7 +46,7 @@ How to make a 1d-histogram in C++ and to fill it:
          *
          * Use wfill(...) if you have to, else prefer fill(...).
          */
-        h.wfill(0.1, 5.0);
+        h.wincrement(0.1, 5.0);
 
         /* Print a table representation of the histogram showing the bin
          * value and a estimate of the standard deviation. Overflow and
@@ -111,7 +111,7 @@ How to make a 2d-histogram in Python and to fill it using a Numpy array:
     rphi = np.empty((1000, 2))
     rphi[:, 0] = (x ** 2 + y ** 2) ** 0.5 # compute radius
     rphi[:, 1] = np.arctan2(y, x)         # compute phi
-    h.fill(rphi)
+    h.increment(rphi)
 
     # access counts as a numpy array (no data is copied)
     count_matrix = np.asarray(h)
diff --git a/examples/example_1d.py b/examples/example_1d.py
index 38ec73e6..e0e7eff5 100644
--- a/examples/example_1d.py
+++ b/examples/example_1d.py
@@ -3,7 +3,7 @@ import numpy as np
 import matplotlib.pyplot as plt
 
 h = hg.histogram(hg.regular_axis(10, -3, 3))
-h.fill(np.random.randn(1000))
+h.increment(np.random.randn(1000))
 
 bins = h.axis(0).bins
 
diff --git a/examples/example_2d.py b/examples/example_2d.py
index b2e98e1b..4fdfb2f1 100644
--- a/examples/example_2d.py
+++ b/examples/example_2d.py
@@ -6,7 +6,7 @@ h = hg.histogram(hg.regular_axis(10, -3, 3, uoflow=False),
                  hg.regular_axis(10, -3, 3, uoflow=False))
 xy = np.random.randn(2000).reshape((1000, 2))
 xy[:,1] *= 0.5
-h.fill(xy)
+h.increment(xy)
 
 bins = h.axis(0).bins
 
diff --git a/include/boost/histogram/dynamic_histogram.hpp b/include/boost/histogram/dynamic_histogram.hpp
index 8056ff4f..e0e3ca4f 100644
--- a/include/boost/histogram/dynamic_histogram.hpp
+++ b/include/boost/histogram/dynamic_histogram.hpp
@@ -133,7 +133,7 @@ public:
   }
 
   template <typename... Values>
-  void fill(Values... values)
+  void increment(Values... values)
   {
     BOOST_ASSERT_MSG(sizeof...(values) == dim(),
                      "number of arguments does not match histogram dimension");
@@ -145,7 +145,7 @@ public:
 
   template <typename Iterator,
             typename = detail::is_iterator<Iterator>>
-  void fill(Iterator begin, Iterator end)
+  void increment(Iterator begin, Iterator end)
   {
     BOOST_ASSERT_MSG(std::distance(begin, end) == dim(),
                      "number of arguments does not match histogram dimension");
@@ -157,16 +157,16 @@ public:
 
   template <typename Sequence,
             typename = detail::is_sequence<Sequence>>
-  void fill(const Sequence& values)
+  void increment(const Sequence& values)
   {
-    fill(std::begin(values), std::end(values));
+    increment(std::begin(values), std::end(values));
   }
 
   template <typename... Values>
-  void wfill(value_type w, Values... values)
+  void wincrement(value_type w, Values... values)
   {
     static_assert(detail::has_weight_support<Storage>::value,
-                  "wfill only supported for adaptive_storage");
+                  "wincrement only supported for adaptive_storage");
     BOOST_ASSERT_MSG(sizeof...(values) == dim(),
                      "number of arguments does not match histogram dimension");
     detail::linearize_x lin;
@@ -177,10 +177,10 @@ public:
 
   template <typename Iterator,
             typename = detail::is_iterator<Iterator>>
-  void wfill(value_type w, Iterator begin, Iterator end)
+  void wincrement(value_type w, Iterator begin, Iterator end)
   {
     static_assert(detail::has_weight_support<Storage>::value,
-                  "wfill only supported for adaptive_storage");
+                  "wincrement only supported for adaptive_storage");
     BOOST_ASSERT_MSG(std::distance(begin, end) == dim(),
                      "iterator range does not match histogram dimension");
     detail::linearize_x lin;
@@ -191,9 +191,9 @@ public:
 
   template <typename Sequence,
             typename = detail::is_sequence<Sequence>>
-  void wfill(value_type w, const Sequence& values)
+  void wincrement(value_type w, const Sequence& values)
   {
-    wfill(w, std::begin(values), std::end(values));
+    wincrement(w, std::begin(values), std::end(values));
   }
 
   template <typename... Indices>
diff --git a/include/boost/histogram/static_histogram.hpp b/include/boost/histogram/static_histogram.hpp
index 6d2f6ec7..e3df6eb5 100644
--- a/include/boost/histogram/static_histogram.hpp
+++ b/include/boost/histogram/static_histogram.hpp
@@ -103,7 +103,7 @@ public:
   }
 
   template <typename... Values>
-  void fill(Values... values)
+  void increment(Values... values)
   {
     static_assert(sizeof...(values) == dim(),
                   "number of arguments does not match histogram dimension");
@@ -115,7 +115,7 @@ public:
 
   template <typename Iterator,
             typename = detail::is_iterator<Iterator>>
-  void fill(Iterator begin, Iterator end)
+  void increment(Iterator begin, Iterator end)
   {
     BOOST_ASSERT_MSG(std::distance(begin, end) == dim(),
                      "iterator range does not match histogram dimension");
@@ -127,16 +127,16 @@ public:
 
   template <typename Sequence,
             typename = detail::is_sequence<Sequence>>
-  void fill(const Sequence& values)
+  void increment(const Sequence& values)
   {
-    fill(std::begin(values), std::end(values));
+    increment(std::begin(values), std::end(values));
   }
 
   template <typename... Values>
-  void wfill(value_type w, Values... values)
+  void wincrement(value_type w, Values... values)
   {
     static_assert(detail::has_weight_support<Storage>::value,
-                  "wfill only supported for adaptive_storage");
+                  "wincrement only supported for adaptive_storage");
     static_assert(sizeof...(values) == dim(),
                   "number of arguments does not match histogram dimension");
     detail::linearize_x lin;
@@ -147,10 +147,10 @@ public:
 
   template <typename Iterator,
             typename = detail::is_iterator<Iterator>>
-  void wfill(value_type w, Iterator begin, Iterator end)
+  void wincrement(value_type w, Iterator begin, Iterator end)
   {
     static_assert(detail::has_weight_support<Storage>::value,
-                  "wfill only supported for adaptive_storage");
+                  "wincrement only supported for adaptive_storage");
     BOOST_ASSERT_MSG(std::distance(begin, end) == dim(),
                      "iterator range does not match histogram dimension");
     detail::linearize_x lin;
@@ -161,9 +161,9 @@ public:
 
   template <typename Sequence,
             typename = detail::is_sequence<Sequence>>
-  void wfill(value_type w, const Sequence& values)
+  void wincrement(value_type w, const Sequence& values)
   {
-    wfill(w, std::begin(values), std::end(values));
+    wincrement(w, std::begin(values), std::end(values));
   }
 
   template <typename... Indices>
diff --git a/src/python/histogram.cpp b/src/python/histogram.cpp
index c3864c20..5f367c1d 100644
--- a/src/python/histogram.cpp
+++ b/src/python/histogram.cpp
@@ -75,7 +75,7 @@ histogram_init(python::tuple args, python::dict kwargs) {
 }
 
 python::object
-histogram_fill(python::tuple args, python::dict kwargs) {
+histogram_increment(python::tuple args, python::dict kwargs) {
   using namespace python;
 
   const unsigned nargs = len(args);
@@ -143,7 +143,7 @@ histogram_fill(python::tuple args, python::dict kwargs) {
           for (unsigned i = 0; i < dims[0]; ++i) {
             double* v = reinterpret_cast<double*>(PyArray_GETPTR1(a, i) );
             double* w = reinterpret_cast<double*>(PyArray_GETPTR1(aw, i));
-            self.wfill(*w, v, v+self.dim());
+            self.wincrement(*w, v, v+self.dim());
           }
 
           Py_DECREF(aw);
@@ -154,7 +154,7 @@ histogram_fill(python::tuple args, python::dict kwargs) {
       } else {
         for (unsigned i = 0; i < dims[0]; ++i) {
           double* v = reinterpret_cast<double*>(PyArray_GETPTR1(a, i));
-          self.fill(v, v+self.dim());
+          self.increment(v, v+self.dim());
         }
       }
 
@@ -175,11 +175,11 @@ histogram_fill(python::tuple args, python::dict kwargs) {
     v[i] = extract<double>(args[1 + i]);
 
   if (ow.is_none()) {
-    self.fill(v, v+self.dim());
+    self.increment(v, v+self.dim());
 
   } else {
     const double w = extract<double>(ow);
-    self.wfill(w, v, v+self.dim());
+    self.wincrement(w, v, v+self.dim());
   }
 
   return object();
@@ -293,10 +293,10 @@ void register_histogram()
        ":param int i: index of the axis\n"
        ":returns: axis object for axis i",
        (arg("self"), arg("i") = 0))
-    .def("fill", raw_function(histogram_fill),
+    .def("increment", raw_function(histogram_increment),
        "Pass a sequence of values with a length n is"
        "\nequal to the dimensions of the histogram,"
-       "\nand optionally a weight w for this fill"
+       "\nand optionally a weight w for this increment"
        "\n(*int* or *float*)."
        "\n"
        "\nIf Numpy support is enabled, values may also"
diff --git a/test/dynamic_histogram_test.cpp b/test/dynamic_histogram_test.cpp
index afb3c5f7..4c58be69 100644
--- a/test/dynamic_histogram_test.cpp
+++ b/test/dynamic_histogram_test.cpp
@@ -125,7 +125,7 @@ int main() {
     {
         auto h = make_dynamic_histogram_with<adaptive_storage<>>(integer_axis(0, 1),
                                                               integer_axis(0, 2));
-        h.fill(0, 0);
+        h.increment(0, 0);
         auto h2 = decltype(h)(h);
         BOOST_TEST(h2 == h);
         auto h3 = dynamic_histogram<
@@ -139,7 +139,7 @@ int main() {
     {
         auto h = make_dynamic_histogram_with<adaptive_storage<>>(integer_axis(0, 1),
                                                                integer_axis(0, 2));
-        h.fill(0, 0);
+        h.increment(0, 0);
         auto h2 = decltype(h)();
         BOOST_TEST(!(h == h2));
         h2 = h;
@@ -159,7 +159,7 @@ int main() {
     {
         auto h = make_dynamic_histogram(integer_axis(0, 1),
                                         integer_axis(0, 2));
-        h.fill(0, 0);
+        h.increment(0, 0);
         const auto href = h;
         decltype(h) h2(std::move(h));
         BOOST_TEST_EQ(h.dim(), 0u);
@@ -195,13 +195,13 @@ int main() {
         auto d = make_dynamic_histogram(regular_axis(2, 0, 1));
         BOOST_TEST(!(c == d));
         BOOST_TEST(!(d == c));
-        c.fill(0);
+        c.increment(0);
         BOOST_TEST(!(a == c));
         BOOST_TEST(!(c == a));
-        a.fill(0);
+        a.increment(0);
         BOOST_TEST(a == c);
         BOOST_TEST(c == a);
-        a.fill(0);
+        a.increment(0);
         BOOST_TEST(!(a == c));
         BOOST_TEST(!(c == a));
     }
@@ -209,10 +209,10 @@ int main() {
     // d1
     {
         auto h = make_dynamic_histogram(integer_axis(0, 1));
-        h.fill(0);
-        h.fill(0);
-        h.fill(-1);
-        h.fill(10);
+        h.increment(0);
+        h.increment(0);
+        h.increment(-1);
+        h.increment(10);
 
         BOOST_TEST_EQ(h.dim(), 1u);
         BOOST_TEST_EQ(bins(h.axis(0)), 2);
@@ -237,10 +237,10 @@ int main() {
     // d1_2
     {
         auto h = make_dynamic_histogram(integer_axis(0, 1, "", false));
-        h.fill(0);
-        h.fill(-0);
-        h.fill(-1);
-        h.fill(10);
+        h.increment(0);
+        h.increment(-0);
+        h.increment(-1);
+        h.increment(10);
 
         BOOST_TEST_EQ(h.dim(), 1u);
         BOOST_TEST_EQ(bins(h.axis(0)), 2);
@@ -261,11 +261,11 @@ int main() {
     // d1w
     {
         auto h = make_dynamic_histogram(regular_axis(2, -1, 1));
-        h.fill(0);
-        h.wfill(2, -1.0);
-        h.fill(-1.0);
-        h.fill(-2.0);
-        h.wfill(5, 10);
+        h.increment(0);
+        h.wincrement(2, -1.0);
+        h.increment(-1.0);
+        h.increment(-2.0);
+        h.wincrement(5, 10);
 
         BOOST_TEST_EQ(h.sum(), 10.0);
 
@@ -284,12 +284,12 @@ int main() {
     {
         auto h = make_dynamic_histogram(regular_axis(2, -1, 1),
                                         integer_axis(-1, 1, nullptr, false));
-        h.fill(-1, -1);
-        h.fill(-1, 0);
+        h.increment(-1, -1);
+        h.increment(-1, 0);
         std::array<double, 2> ai = {{-1., -10.}};
-        h.fill(ai);
+        h.increment(ai);
         double in[2] = {-10., 0.};
-        h.fill(in, in+2);
+        h.increment(in, in+2);
 
         BOOST_TEST_EQ(h.dim(), 2u);
         BOOST_TEST_EQ(bins(h.axis(0)), 2);
@@ -335,10 +335,10 @@ int main() {
     {
         auto h = make_dynamic_histogram(regular_axis(2, -1, 1),
                                         integer_axis(-1, 1, nullptr, false));
-        h.fill(-1, 0);       // -> 0, 1
-        h.wfill(10, -1, -1); // -> 0, 0
-        h.wfill(5, -1, -10); // is ignored
-        h.wfill(7, -10, 0);  // -> -1, 1
+        h.increment(-1, 0);       // -> 0, 1
+        h.wincrement(10, -1, -1); // -> 0, 0
+        h.wincrement(5, -1, -10); // is ignored
+        h.wincrement(7, -10, 0);  // -> -1, 1
 
         BOOST_TEST_EQ(h.sum(), 18.0);
 
@@ -384,7 +384,7 @@ int main() {
             for (auto j = 0; j < bins(h.axis(1)); ++j)
                 for (auto k = 0; k < bins(h.axis(2)); ++k)
         {
-            h.wfill(i+j+k, i, j, k);
+            h.wincrement(i+j+k, i, j, k);
         }
 
         for (auto i = 0; i < bins(h.axis(0)); ++i)
@@ -412,8 +412,8 @@ int main() {
                 mpl::vector<integer_axis, regular_axis>,
                 container_storage<std::vector<unsigned>>
             >(integer_axis(-1, 1));
-        a.fill(-1);
-        b.fill(1);
+        a.increment(-1);
+        b.increment(1);
         auto c = a;
         c += b;
         BOOST_TEST_EQ(c.value(-1), 0);
@@ -435,8 +435,8 @@ int main() {
         auto a = make_dynamic_histogram(integer_axis(-1, 1));
         auto b = make_dynamic_histogram(integer_axis(-1, 1));
 
-        a.fill(0);
-        b.wfill(3, -1);
+        a.increment(0);
+        b.wincrement(3, -1);
         auto c = a;
         c += b;
         BOOST_TEST_EQ(c.value(-1), 0);
@@ -457,8 +457,8 @@ int main() {
     {
         auto a = make_dynamic_histogram_with<container_storage<std::vector<unsigned char>>>(integer_axis(-1, 1));
         auto b = make_dynamic_histogram_with<container_storage<std::vector<unsigned>>>(integer_axis(-1, 1));
-        a.fill(-1);
-        b.fill(1);
+        a.increment(-1);
+        b.increment(1);
         auto c = a;
         c += b;
         BOOST_TEST_EQ(c.value(-1), 0u);
@@ -501,7 +501,7 @@ int main() {
                                         variable_axis({0.1, 0.2, 0.3, 0.4, 0.5}, "v"),
                                         category_axis{"A", "B", "C"},
                                         integer_axis(0, 1, "i"));
-        a.fill(0.5, 0.1, 0.25, 1, 0);
+        a.increment(0.5, 0.1, 0.25, 1, 0);
         std::string buf;
         {
             std::ostringstream os;
diff --git a/test/python_suite_test.py.in b/test/python_suite_test.py.in
index d7ae9358..a6688154 100755
--- a/test/python_suite_test.py.in
+++ b/test/python_suite_test.py.in
@@ -349,17 +349,17 @@ class histogramest(unittest.TestCase):
         h1 = histogram(integer_axis(-1, 1, uoflow=True))
         for h in (h0, h1):
             with self.assertRaises(RuntimeError):
-                h.fill()
+                h.increment()
             with self.assertRaises(RuntimeError):
-                h.fill(1, 2)
-            h.fill(-10)
-            h.fill(-1)
-            h.fill(-1)
-            h.fill(0)
-            h.fill(1)
-            h.fill(1)
-            h.fill(1)
-            h.fill(10)
+                h.increment(1, 2)
+            h.increment(-10)
+            h.increment(-1)
+            h.increment(-1)
+            h.increment(0)
+            h.increment(1)
+            h.increment(1)
+            h.increment(1)
+            h.increment(10)
         self.assertEqual(h0.sum, 6)
         self.assertEqual(h0.axis(0).shape, 3)
         self.assertEqual(h1.sum, 8)
@@ -386,14 +386,14 @@ class histogramest(unittest.TestCase):
 
     def test_growth(self):
         h = histogram(integer_axis(-1, 1))
-        h.fill(-1)
-        h.fill(1)
-        h.fill(1)
+        h.increment(-1)
+        h.increment(1)
+        h.increment(1)
         for i in range(255):
-            h.fill(0)
-        h.fill(0)
+            h.increment(0)
+        h.increment(0)
         for i in range(1000-256):
-            h.fill(0)
+            h.increment(0)
         self.assertEqual(h.value(-1), 0)
         self.assertEqual(h.value(0), 1)
         self.assertEqual(h.value(1), 1000)
@@ -404,17 +404,17 @@ class histogramest(unittest.TestCase):
         for uoflow in (False, True):
             h = histogram(integer_axis(-1, 1, uoflow=uoflow),
                            regular_axis(4, -2, 2, uoflow=uoflow))
-            h.fill(-1, -2)
-            h.fill(-1, -1)
-            h.fill(0, 0)
-            h.fill(0, 1)
-            h.fill(1, 0)
-            h.fill(3, -1)
-            h.fill(0, -3)
+            h.increment(-1, -2)
+            h.increment(-1, -1)
+            h.increment(0, 0)
+            h.increment(0, 1)
+            h.increment(1, 0)
+            h.increment(3, -1)
+            h.increment(0, -3)
             with self.assertRaises(Exception):
-                h.fill(1)
+                h.increment(1)
             with self.assertRaises(Exception):
-                h.fill(1, 2, 3)
+                h.increment(1, 2, 3)
 
             m = [[1, 1, 0, 0, 0, 0],
                  [0, 0, 1, 1, 0, 1],
@@ -429,13 +429,13 @@ class histogramest(unittest.TestCase):
         for uoflow in (False, True):
             h = histogram(integer_axis(-1, 1, uoflow=uoflow),
                           regular_axis(4, -2, 2, uoflow=uoflow))
-            h.fill(-1, -2)
-            h.fill(-1, -1)
-            h.fill(0, 0)
-            h.fill(0, 1)
-            h.fill(1, 0)
-            h.fill(3, -1)
-            h.fill(0, -3)
+            h.increment(-1, -2)
+            h.increment(-1, -1)
+            h.increment(0, 0)
+            h.increment(0, 1)
+            h.increment(1, 0)
+            h.increment(3, -1)
+            h.increment(0, -3)
 
             m = [[1, 1, 0, 0, 0, 0],
                  [0, 0, 1, 1, 0, 1],
@@ -460,13 +460,13 @@ class histogramest(unittest.TestCase):
         for uoflow in (False, True):
             h = histogram(integer_axis(-1, 1, uoflow=uoflow),
                           regular_axis(4, -2, 2, uoflow=uoflow))
-            h.fill(-1, -2)
-            h.fill(-1, -1)
-            h.fill(0, 0)
-            h.fill(0, 1)
-            h.fill(1, 0)
-            h.fill(3, -1)
-            h.fill(0, -3)
+            h.increment(-1, -2)
+            h.increment(-1, -1)
+            h.increment(0, 0)
+            h.increment(0, 1)
+            h.increment(1, 0)
+            h.increment(3, -1)
+            h.increment(0, -3)
 
             m = [[1, 1, 0, 0, 0, 0],
                  [0, 0, 1, 1, 0, 1],
@@ -476,7 +476,7 @@ class histogramest(unittest.TestCase):
 
             h2 = histogram(integer_axis(-1, 1, uoflow=uoflow),
                            regular_axis(4, -2, 2, uoflow=uoflow))
-            h2.fill(0, 0, w=0)
+            h2.increment(0, 0, w=0)
 
             h2 += h
             h2 += h
@@ -495,15 +495,15 @@ class histogramest(unittest.TestCase):
                       variable_axis(0.0, 1.0, 2.0),
                       polar_axis(4, label='pa'))
         for i in range(a.axis(0).bins):
-            a.fill(i, 0, 0, 0, 0)
+            a.increment(i, 0, 0, 0, 0)
             for j in range(a.axis(1).bins):
-                a.fill(i, j, 0, 0, 0)
+                a.increment(i, j, 0, 0, 0)
                 for k in range(a.axis(2).bins):
-                    a.fill(i, j, k, 0, 0)
+                    a.increment(i, j, k, 0, 0)
                     for l in range(a.axis(3).bins):
-                        a.fill(i, j, k, l, 0)
+                        a.increment(i, j, k, l, 0)
                         for m in range(a.axis(4).bins):
-                            a.fill(i, j, k, l, m * 0.5 * pi)
+                            a.increment(i, j, k, l, m * 0.5 * pi)
 
         io = BytesIO()
         pickle.dump(a, io)
@@ -525,13 +525,13 @@ class histogramest(unittest.TestCase):
                        regular_axis(4, 0.0, 4.0, uoflow=False),
                        variable_axis(0.0, 1.0, 2.0))
         for i in range(a.axis(0).bins):
-            a.fill(i, 0, 0, 0, w=3)
+            a.increment(i, 0, 0, 0, w=3)
             for j in range(a.axis(1).bins):
-                a.fill(i, j, 0, 0, w=10)
+                a.increment(i, j, 0, 0, w=10)
                 for k in range(a.axis(2).bins):
-                    a.fill(i, j, k, 0, w=2)
+                    a.increment(i, j, k, 0, w=2)
                     for l in range(a.axis(3).bins):
-                        a.fill(i, j, k, l, w=5)
+                        a.increment(i, j, k, l, w=5)
 
         io = BytesIO()
         pickle.dump(a, io)
@@ -550,7 +550,7 @@ class histogramest(unittest.TestCase):
     def test_numpy_conversion_0(self):
         a = histogram(integer_axis(0, 2, uoflow=False))
         for i in range(100):
-            a.fill(1)
+            a.increment(1)
         c = numpy.array(a) # a copy
         v = numpy.asarray(a) # a view
 
@@ -559,12 +559,12 @@ class histogramest(unittest.TestCase):
             self.assertTrue(numpy.all(t == numpy.array((0, 100, 0))))
 
         for i in range(100):
-            a.fill(1)
+            a.increment(1)
         self.assertTrue(numpy.all(c == numpy.array((0, 100, 0))))
         self.assertTrue(numpy.all(v == numpy.array((0, 200, 0))))
 
         for i in range(100):
-            a.fill(1)
+            a.increment(1)
         c = numpy.array(a)
         self.assertEqual(c.dtype, numpy.uint16)
         self.assertTrue(numpy.all(c == numpy.array((0, 300, 0))))
@@ -575,7 +575,7 @@ class histogramest(unittest.TestCase):
     def test_numpy_conversion_1(self):
         a = histogram(integer_axis(0, 2))
         for i in range(10):
-            a.fill(1, w=3)
+            a.increment(1, w=3)
         c = numpy.array(a) # a copy
         v = numpy.asarray(a) # a view
         self.assertEqual(c.dtype, numpy.float64)
@@ -592,7 +592,7 @@ class histogramest(unittest.TestCase):
             for j in range(a.axis(1).bins):
                 for k in range(a.axis(2).bins):
                     for m in range(i+j+k):
-                        a.fill(i, j, k)
+                        a.increment(i, j, k)
                     r[i,j,k] = i+j+k
         c = numpy.array(a) # a copy
         v = numpy.asarray(a) # a view
@@ -616,7 +616,7 @@ class histogramest(unittest.TestCase):
         for i in range(a.axis(0).bins):
             for j in range(a.axis(1).bins):
                 for k in range(a.axis(2).bins):
-                    a.fill(i, j, k, w=i+j+k)
+                    a.increment(i, j, k, w=i+j+k)
                     r[0, i, j, k] = i+j+k
                     r[1, i, j, k] = (i+j+k)**2
         c = numpy.array(a) # a copy
@@ -636,7 +636,7 @@ class histogramest(unittest.TestCase):
     @unittest.skipUnless(have_numpy, "requires build with numpy-support")
     def test_bad_numpy_conversion(self):
         a = histogram(integer_axis(0, 0))
-        a.fill(0)
+        a.increment(0)
         for i in xrange(80):
             a += a
         # a now holds a multiprecision type
@@ -646,36 +646,36 @@ class histogramest(unittest.TestCase):
     @unittest.skipUnless(have_numpy, "requires build with numpy-support")
     def test_fill_with_numpy_array_0(self):
         a = histogram(integer_axis(0, 2, uoflow=False))
-        a.fill(numpy.array([-1, 0, 1, 2, 1, 4]))
-        a.fill((-1, 0))
-        a.fill([1, 2])
+        a.increment(numpy.array([-1, 0, 1, 2, 1, 4]))
+        a.increment((-1, 0))
+        a.increment([1, 2])
         self.assertEqual(a.value(0), 2)
         self.assertEqual(a.value(1), 3)
         self.assertEqual(a.value(2), 2)
 
         with self.assertRaises(ValueError):
-            a.fill(numpy.empty((2, 2)))
+            a.increment(numpy.empty((2, 2)))
         with self.assertRaises(ValueError):
-            a.fill(numpy.empty((1, 2, 2)))
+            a.increment(numpy.empty((1, 2, 2)))
         with self.assertRaises(RuntimeError):
-            a.fill(numpy.empty((2, 1)), 1)
+            a.increment(numpy.empty((2, 1)), 1)
         with self.assertRaises(ValueError):
-            a.fill("abc")
+            a.increment("abc")
 
         a = histogram(integer_axis(0, 1, uoflow=False),
                       regular_axis(2, 0, 2, uoflow=False))
-        a.fill(numpy.array([[-1., -1.], [0., 1.], [1., 0.1]]))
+        a.increment(numpy.array([[-1., -1.], [0., 1.], [1., 0.1]]))
         self.assertEqual(a.value(0, 0), 0)
         self.assertEqual(a.value(0, 1), 1)
         self.assertEqual(a.value(1, 0), 1)
         self.assertEqual(a.value(1, 1), 0)
 
         with self.assertRaises(ValueError):
-            a.fill((1, 2, 3))
+            a.increment((1, 2, 3))
 
         a = histogram(integer_axis(0, 2, uoflow=False))
-        a.fill([0, 0, 1, 2])
-        a.fill((1, 0, 2, 2))
+        a.increment([0, 0, 1, 2])
+        a.increment((1, 0, 2, 2))
         self.assertEqual(a.value(0), 3)
         self.assertEqual(a.value(1), 2)
         self.assertEqual(a.value(2), 3)
@@ -686,8 +686,8 @@ class histogramest(unittest.TestCase):
         a = histogram(integer_axis(0, 2, uoflow=True))
         v = numpy.array([-1, 0, 1, 2, 3, 4])
         w = numpy.array([ 2, 3, 4, 5, 6, 7])
-        a.fill(v, w=w)
-        a.fill([0, 1], w=[2.0, 3.0])
+        a.increment(v, w=w)
+        a.increment([0, 1], w=[2.0, 3.0])
         self.assertEqual(a.value(-1), 2)
         self.assertEqual(a.value(0), 5)
         self.assertEqual(a.value(1), 7)
@@ -698,28 +698,28 @@ class histogramest(unittest.TestCase):
         self.assertEqual(a.variance(2), 25)
 
         with self.assertRaises(RuntimeError):
-            a.fill([1, 2], foo=[1, 1])
+            a.increment([1, 2], foo=[1, 1])
         with self.assertRaises(ValueError):
-            a.fill([1, 2], w=[1])
+            a.increment([1, 2], w=[1])
         with self.assertRaises(ValueError):
-            a.fill([1, 2], w="ab")
+            a.increment([1, 2], w="ab")
         with self.assertRaises(ValueError):
-            a.fill([1, 2], w=1)
+            a.increment([1, 2], w=1)
         with self.assertRaises(RuntimeError):
-            a.fill([1, 2], w=[1, 1], foo=1)
+            a.increment([1, 2], w=[1, 1], foo=1)
         with self.assertRaises(ValueError):
-            a.fill([1, 2], w=[[1, 1], [2, 2]])
+            a.increment([1, 2], w=[[1, 1], [2, 2]])
 
         a = histogram(integer_axis(0, 1, uoflow=False),
                       regular_axis(2, 0, 2, uoflow=False))
-        a.fill(numpy.array([[-1., -1.], [0., 1.], [1., 0.1]]))
+        a.increment(numpy.array([[-1., -1.], [0., 1.], [1., 0.1]]))
         self.assertEqual(a.value(0, 0), 0)
         self.assertEqual(a.value(0, 1), 1)
         self.assertEqual(a.value(1, 0), 1)
         self.assertEqual(a.value(1, 1), 0)
         a = histogram(integer_axis(0, 2, uoflow=False))
-        a.fill([0, 0, 1, 2])
-        a.fill((1, 0, 2, 2))
+        a.increment([0, 0, 1, 2])
+        a.increment((1, 0, 2, 2))
         self.assertEqual(a.value(0), 3)
         self.assertEqual(a.value(1), 2)
         self.assertEqual(a.value(2), 3)
diff --git a/test/speed_cpp.cpp b/test/speed_cpp.cpp
index 3710c49b..e52339d6 100644
--- a/test/speed_cpp.cpp
+++ b/test/speed_cpp.cpp
@@ -46,7 +46,7 @@ double compare_1d(unsigned n, int distrib)
     auto h = Histogram(regular_axis(100, 0, 1));
     auto t = clock();
     for (unsigned i = 0; i < n; ++i)
-      h.fill(r[i]);
+      h.increment(r[i]);
     t = clock() - t;
     best = std::min(best, double(t) / CLOCKS_PER_SEC);
   }
@@ -66,7 +66,7 @@ double compare_3d(unsigned n, int distrib)
                        regular_axis(100, 0, 1));
     auto t = clock();
     for (unsigned i = 0; i < n; ++i)
-      h.fill(r[3 * i], r[3 * i + 1], r[3 * i + 2]);
+      h.increment(r[3 * i], r[3 * i + 1], r[3 * i + 2]);
     t = clock() - t;
     best = std::min(best, double(t) / CLOCKS_PER_SEC);
   } 
@@ -94,7 +94,7 @@ double compare_6d(unsigned n, int distrib)
     for (unsigned i = 0; i < n; ++i) {
       for (unsigned k = 0; k < 6; ++k)
         x[k] = r[6 * i + k];      
-      h.fill(x[0], x[1], x[2], x[3], x[4], x[5]);
+      h.increment(x[0], x[1], x[2], x[3], x[4], x[5]);
     }
     t = clock() - t;
     best = std::min(best, double(t) / CLOCKS_PER_SEC);
diff --git a/test/speed_vs_numpy.py b/test/speed_vs_numpy.py
index 169d34d3..fb5ff32b 100755
--- a/test/speed_vs_numpy.py
+++ b/test/speed_vs_numpy.py
@@ -26,7 +26,7 @@ def compare_1d(n, distrib):
 
         h = histogram(regular_axis(100, 0, 1))
         t = timer()
-        h.fill(r)
+        h.increment(r)
         t = timer() - t
         best_boost = min(t, best_boost)
     assert(np.all(w == np.array(h)[:-2]))
@@ -57,7 +57,7 @@ def compare_3d(n, distrib):
                       regular_axis(100, 0, 1),
                       regular_axis(100, 0, 1))
         t = timer()
-        h.fill(r)
+        h.increment(r)
         t = timer() - t
         best_boost = min(t, best_boost)
     assert(np.all(w == np.array(h)[:-2,:-2,:-2]))
@@ -95,7 +95,7 @@ def compare_6d(n, distrib):
                       regular_axis(10, 0, 1),
                       regular_axis(10, 0, 1))
         t = timer()
-        h.fill(r)
+        h.increment(r)
         t = timer() - t
         best_boost = min(t, best_boost)
     assert(np.all(w == np.array(h)[:-2,:-2,:-2,:-2,:-2,:-2]))
diff --git a/test/static_histogram_test.cpp b/test/static_histogram_test.cpp
index 0a5a8897..725f088f 100644
--- a/test/static_histogram_test.cpp
+++ b/test/static_histogram_test.cpp
@@ -113,7 +113,7 @@ int main() {
     {
         auto h = make_static_histogram(integer_axis(0, 1),
                                        integer_axis(0, 2));
-        h.fill(0, 0);
+        h.increment(0, 0);
         auto h2 = decltype(h)(h);
         BOOST_TEST(h2 == h);
         auto h3 = static_histogram<
@@ -127,7 +127,7 @@ int main() {
     {
         auto h = make_static_histogram(integer_axis(0, 1),
                                        integer_axis(0, 2));
-        h.fill(0, 0);
+        h.increment(0, 0);
         auto h2 = decltype(h)();
         BOOST_TEST(!(h == h2));
         h2 = h;
@@ -147,7 +147,7 @@ int main() {
     {
         auto h = make_static_histogram(integer_axis(0, 1),
                                        integer_axis(0, 2));
-        h.fill(0, 0);
+        h.increment(0, 0);
         const auto href = h;
         decltype(h) h2(std::move(h));
         BOOST_TEST_EQ(h.dim(), 2);
@@ -176,13 +176,13 @@ int main() {
         auto d = make_static_histogram(regular_axis(2, 0, 1));
         BOOST_TEST(!(c == d));
         BOOST_TEST(!(d == c));
-        c.fill(0);
+        c.increment(0);
         BOOST_TEST(!(a == c));
         BOOST_TEST(!(c == a));
-        a.fill(0);
+        a.increment(0);
         BOOST_TEST(a == c);
         BOOST_TEST(c == a);
-        a.fill(0);
+        a.increment(0);
         BOOST_TEST(!(a == c));
         BOOST_TEST(!(c == a));
     }
@@ -190,10 +190,10 @@ int main() {
     // d1
     {
         auto h = make_static_histogram(integer_axis(0, 1));
-        h.fill(0);
-        h.fill(0);
-        h.fill(-1);
-        h.fill(10);
+        h.increment(0);
+        h.increment(0);
+        h.increment(-1);
+        h.increment(10);
 
         BOOST_TEST_EQ(h.dim(), 1);
         BOOST_TEST_EQ(bins(h.axis<0>()), 2);
@@ -218,10 +218,10 @@ int main() {
     // d1_2
     {
         auto h = make_static_histogram(integer_axis(0, 1, "", false));
-        h.fill(0);
-        h.fill(-0);
-        h.fill(-1);
-        h.fill(10);
+        h.increment(0);
+        h.increment(-0);
+        h.increment(-1);
+        h.increment(10);
 
         BOOST_TEST_EQ(h.dim(), 1);
         BOOST_TEST_EQ(bins(h.axis<0>()), 2);
@@ -242,11 +242,11 @@ int main() {
     // d1w
     {
         auto h = make_static_histogram(regular_axis(2, -1, 1));
-        h.fill(0);
-        h.wfill(2.0, -1.0);
-        h.fill(-1.0);
-        h.fill(-2.0);
-        h.wfill(5.0, 10.0);
+        h.increment(0);
+        h.wincrement(2.0, -1.0);
+        h.increment(-1.0);
+        h.increment(-2.0);
+        h.wincrement(5.0, 10.0);
 
         BOOST_TEST_EQ(h.sum(), 10);
 
@@ -265,12 +265,12 @@ int main() {
     {
         auto h = make_static_histogram(regular_axis(2, -1, 1),
                                        integer_axis(-1, 1, "", false));
-        h.fill(-1, -1);
-        h.fill(-1, 0);
+        h.increment(-1, -1);
+        h.increment(-1, 0);
         std::array<double, 2> ai = {{-1., -10.}};
-        h.fill(ai);
+        h.increment(ai);
         double in[2] = {-10., 0.};
-        h.fill(in, in+2);
+        h.increment(in, in+2);
 
         BOOST_TEST_EQ(h.dim(), 2);
         BOOST_TEST_EQ(bins(h.axis<0>()), 2);
@@ -316,10 +316,10 @@ int main() {
     {
         auto h = make_static_histogram(regular_axis(2, -1, 1),
                                        integer_axis(-1, 1, "", false));
-        h.fill(-1, 0);       // -> 0, 1
-        h.wfill(10, -1, -1); // -> 0, 0
-        h.wfill(5, -1, -10); // is ignored
-        h.wfill(7, -10, 0);  // -> -1, 1
+        h.increment(-1, 0);       // -> 0, 1
+        h.wincrement(10, -1, -1); // -> 0, 0
+        h.wincrement(5, -1, -10); // is ignored
+        h.wincrement(7, -10, 0);  // -> -1, 1
 
         BOOST_TEST_EQ(h.sum(), 18);
 
@@ -365,7 +365,7 @@ int main() {
             for (auto j = 0; j < bins(h.axis<1>()); ++j)
                 for (auto k = 0; k < bins(h.axis<2>()); ++k)
         {
-            h.wfill(i+j+k, i, j, k);
+            h.wincrement(i+j+k, i, j, k);
         }
 
         for (auto i = 0; i < bins(h.axis<0>()); ++i)
@@ -382,8 +382,8 @@ int main() {
         auto b = make_static_histogram_with<
           container_storage<std::vector<unsigned>>
         >(integer_axis(-1, 1));
-        a.fill(-1);
-        b.fill(1);
+        a.increment(-1);
+        b.increment(1);
         auto c = a;
         c += b;
         BOOST_TEST_EQ(c.value(-1), 0);
@@ -409,8 +409,8 @@ int main() {
           adaptive_storage<>
         >(integer_axis(-1, 1));
 
-        a.fill(0);
-        b.wfill(3, -1);
+        a.increment(0);
+        b.wincrement(3, -1);
         auto c = a;
         c += b;
         BOOST_TEST_EQ(c.value(-1), 0);
@@ -435,8 +435,8 @@ int main() {
         auto b = make_static_histogram_with<
           container_storage<std::vector<unsigned>>
         >(integer_axis(-1, 1));
-        a.fill(-1);
-        b.fill(1);
+        a.increment(-1);
+        b.increment(1);
         auto c = a;
         c += b;
         BOOST_TEST_EQ(c.value(-1), 0);
@@ -478,15 +478,15 @@ int main() {
         auto h = bh::make_static_histogram(bh::regular_axis(10, -1.0, 2.0, "x"));
 
         // fill histogram with data
-        h.fill(-1.5); // put in underflow bin
-        h.fill(-1.0); // included in first bin, bin interval is semi-open
-        h.fill(-0.5);
-        h.fill(1.1);
-        h.fill(0.3);
-        h.fill(1.7);
-        h.fill(2.0);  // put in overflow bin, bin interval is semi-open
-        h.fill(20.0); // put in overflow bin
-        h.wfill(5.0, 0.1); // fill with a weighted entry, weight is 5.0
+        h.increment(-1.5); // put in underflow bin
+        h.increment(-1.0); // included in first bin, bin interval is semi-open
+        h.increment(-0.5);
+        h.increment(1.1);
+        h.increment(0.3);
+        h.increment(1.7);
+        h.increment(2.0);  // put in overflow bin, bin interval is semi-open
+        h.increment(20.0); // put in overflow bin
+        h.wincrement(5.0, 0.1); // fill with a weighted entry, weight is 5.0
 
         std::ostringstream os1;
         // access histogram counts
@@ -522,7 +522,7 @@ int main() {
                                        variable_axis({0.1, 0.2, 0.3, 0.4, 0.5}, "v"),
                                        category_axis{"A", "B", "C"},
                                        integer_axis(0, 1, "i"));
-        a.fill(0.5, 0.1, 0.25, 1, 0);
+        a.increment(0.5, 0.1, 0.25, 1, 0);
         std::string buf;
         {
             std::ostringstream os;