diff --git a/include/boost/histogram/detail/axes.hpp b/include/boost/histogram/detail/axes.hpp
index 9058ce17..f0da6834 100644
--- a/include/boost/histogram/detail/axes.hpp
+++ b/include/boost/histogram/detail/axes.hpp
@@ -16,6 +16,7 @@
 #include <boost/mp11.hpp>
 #include <boost/variant/apply_visitor.hpp>
 #include <boost/variant/static_visitor.hpp>
+#include <stdexcept>
 #include <tuple>
 #include <type_traits>
 #include <vector>
@@ -577,12 +578,18 @@ optional_index call_impl(dynamic_container_tag, const dynamic_axes<Ts...>& axes,
   return i;
 }
 
+/* In all at_impl, we throw instead of asserting when an index is out of
+ * bounds, because wrapping code cannot check this condition without spending
+ * a lot of extra cycles. For the wrapping code it is much easier to catch
+ * the exception and do something sensible.
+ */
+
 template <typename A, typename... Us>
 std::size_t at_impl(detail::no_container_tag, const A& axes, const Us&... us) {
   dimension_check(axes, mp11::mp_size_t<sizeof...(Us)>());
   auto index = detail::optional_index();
   detail::indices_to_index<0>(index, axes, static_cast<int>(us)...);
-  BOOST_ASSERT_MSG(index, "indices out of bounds");
+  if (!index) throw std::out_of_range("indices out of bounds");
   return *index;
 }
 
@@ -591,7 +598,7 @@ std::size_t at_impl(detail::static_container_tag, const A& axes, const U& u) {
   dimension_check(axes, mp_size<U>());
   auto index = detail::optional_index();
   detail::indices_to_index_get(mp_size<U>(), index, axes, u);
-  BOOST_ASSERT_MSG(index, "indices out of bounds");
+  if (!index) throw std::out_of_range("indices out of bounds");
   return *index;
 }
 
@@ -602,7 +609,7 @@ std::size_t at_impl(detail::dynamic_container_tag, const static_axes<Ts...>& axe
   auto index = detail::optional_index();
   detail::indices_to_index_iter(mp11::mp_size_t<sizeof...(Ts)>(), index, axes,
                                 std::begin(u));
-  BOOST_ASSERT_MSG(index, "indices out of bounds");
+  if (!index) throw std::out_of_range("indices out of bounds");
   return *index;
 }
 
@@ -612,7 +619,7 @@ std::size_t at_impl(detail::dynamic_container_tag, const dynamic_axes<Ts...>& ax
   dimension_check(axes, std::distance(std::begin(u), std::end(u)));
   auto index = detail::optional_index();
   detail::indices_to_index_iter(index, axes, std::begin(u));
-  BOOST_ASSERT_MSG(index, "indices out of bounds");
+  if (!index) throw std::out_of_range("indices out of bounds");
   return *index;
 }
 
diff --git a/include/boost/histogram/histogram.hpp b/include/boost/histogram/histogram.hpp
index aaf3b342..bfd1de50 100644
--- a/include/boost/histogram/histogram.hpp
+++ b/include/boost/histogram/histogram.hpp
@@ -7,6 +7,7 @@
 #ifndef _BOOST_HISTOGRAM_HISTOGRAM_HPP_
 #define _BOOST_HISTOGRAM_HISTOGRAM_HPP_
 
+#include <algorithm>
 #include <boost/assert.hpp>
 #include <boost/histogram/arithmetic_operators.hpp>
 #include <boost/histogram/detail/axes.hpp>
@@ -18,6 +19,7 @@
 #include <boost/histogram/storage/operators.hpp>
 #include <boost/histogram/storage/weight_counter.hpp>
 #include <boost/mp11.hpp>
+#include <functional>
 #include <tuple>
 #include <type_traits>
 #include <utility>
@@ -213,18 +215,21 @@ public:
     return hr;
   }
 
+  // precondition: range represents sequence of strictly ascending axis indices
   template <typename Iterator, typename U = axes_type,
             typename = detail::requires_dynamic_axes<U>,
             typename = detail::requires_iterator<Iterator>>
   histogram reduce_to(Iterator begin, Iterator end) const {
-    std::set<unsigned> indices(begin, end);
-    BOOST_ASSERT_MSG(*indices.rbegin() < dim(), "index out of range");
+    BOOST_ASSERT_MSG(std::is_sorted(begin, end, std::less_equal<decltype(*begin)>()),
+                     "integer sequence must be strictly ascending");
+    BOOST_ASSERT_MSG(begin == end || static_cast<unsigned>(*(end - 1)) < dim(),
+                     "index out of range");
     auto sub_axes = histogram::axes_type(axes_.get_allocator());
-    sub_axes.reserve(indices.size());
+    sub_axes.reserve(std::distance(begin, end));
     auto b = std::vector<bool>(dim(), false);
-    for (auto k : indices) {
-      sub_axes.push_back(axes_[k]);
-      b[k] = true;
+    for (auto it = begin; it != end; ++it) {
+      sub_axes.push_back(axes_[*it]);
+      b[*it] = true;
     }
     auto hr = histogram(std::move(sub_axes), storage_type(storage_.get_allocator()));
     std::vector<unsigned> shape(dim());
diff --git a/src/python/axis.cpp b/src/python/axis.cpp
index 4d3ab020..85e0c04b 100644
--- a/src/python/axis.cpp
+++ b/src/python/axis.cpp
@@ -146,7 +146,7 @@ bp::str axis_get_label(const T& t) {
 
 template <typename A>
 bp::object axis_getitem(const A& a, int i) {
-  if (i < -1 * a.uoflow() || i >= a.size() + 1 * a.uoflow())
+  if (i < -(a.uoflow() == 2) || i >= (a.size() + int(a.uoflow() > 0)))
     throw std::out_of_range("index out of bounds");
   return bp::make_tuple(a.lower(i), a.lower(i + 1));
 }
diff --git a/src/python/histogram.cpp b/src/python/histogram.cpp
index cbeb95d8..814339a5 100644
--- a/src/python/histogram.cpp
+++ b/src/python/histogram.cpp
@@ -316,9 +316,6 @@ bp::object histogram_reduce_to(bp::tuple args, bp::dict kwargs) {
 
   const auto nargs = bp::len(args) - 1;
   if (nargs == 0) { throw std::invalid_argument("at least one argument required"); }
-  if (nargs < self.dim()) {
-    throw std::invalid_argument("fewer arguments than histogram axes required");
-  }
 
   if (nargs > BOOST_HISTOGRAM_AXIS_LIMIT) {
     throw std::invalid_argument(
@@ -327,7 +324,11 @@ bp::object histogram_reduce_to(bp::tuple args, bp::dict kwargs) {
   }
 
   int idx[BOOST_HISTOGRAM_AXIS_LIMIT];
-  for (auto i = 0u; i < nargs; ++i) idx[i] = bp::extract<int>(args[1 + i]);
+  for (auto i = 0u; i < nargs; ++i) {
+    idx[i] = bp::extract<int>(args[1 + i]);
+    if (i > 0 && idx[i] <= idx[i - 1])
+      throw std::invalid_argument("indices must be strictly ascending");
+  }
 
   return bp::object(self.reduce_to(idx, idx + nargs));
 }
diff --git a/src/python/module.cpp b/src/python/module.cpp
index c57ea2e2..8639b725 100644
--- a/src/python/module.cpp
+++ b/src/python/module.cpp
@@ -7,6 +7,7 @@
 #include <boost/python/module.hpp>
 #include <boost/python/object.hpp>
 #include <boost/python/scope.hpp>
+#include <stdexcept>
 #ifdef HAVE_NUMPY
 #include <boost/python/numpy.hpp>
 #endif
@@ -16,6 +17,10 @@ void register_histogram();
 
 BOOST_PYTHON_MODULE(histogram) {
   using namespace boost::python;
+
+  register_exception_translator<std::out_of_range>(
+      [](const std::out_of_range& e) { PyErr_SetString(PyExc_IndexError, e.what()); });
+
   scope current;
 #ifdef HAVE_NUMPY
   numpy::initialize();
diff --git a/test/fail_histogram_dynamic_bin_1_test.cpp b/test/fail_histogram_dynamic_at_tuple_wrong_dimension_test.cpp
similarity index 73%
rename from test/fail_histogram_dynamic_bin_1_test.cpp
rename to test/fail_histogram_dynamic_at_tuple_wrong_dimension_test.cpp
index 4a86e789..c5389157 100644
--- a/test/fail_histogram_dynamic_bin_1_test.cpp
+++ b/test/fail_histogram_dynamic_at_tuple_wrong_dimension_test.cpp
@@ -1,7 +1,8 @@
 #include <boost/histogram.hpp>
+#include <utility>
 
 using namespace boost::histogram;
 int main() {
   auto h = make_dynamic_histogram(axis::integer<>(0, 2));
-  h.at(-2);
+  h.at(std::make_pair(0, 0));
 }
diff --git a/test/fail_histogram_dynamic_at_vector_wrong_dimension_test.cpp b/test/fail_histogram_dynamic_at_vector_wrong_dimension_test.cpp
new file mode 100644
index 00000000..bb5eb0bc
--- /dev/null
+++ b/test/fail_histogram_dynamic_at_vector_wrong_dimension_test.cpp
@@ -0,0 +1,8 @@
+#include <boost/histogram.hpp>
+#include <vector>
+
+using namespace boost::histogram;
+int main() {
+  auto h = make_dynamic_histogram(axis::integer<>(0, 2));
+  h.at(std::vector<int>({0, 0}));
+}
diff --git a/test/fail_histogram_dynamic_bin_0_test.cpp b/test/fail_histogram_dynamic_at_wrong_dimension_test.cpp
similarity index 100%
rename from test/fail_histogram_dynamic_bin_0_test.cpp
rename to test/fail_histogram_dynamic_at_wrong_dimension_test.cpp
diff --git a/test/fail_histogram_dynamic_bin_2_test.cpp b/test/fail_histogram_dynamic_bin_2_test.cpp
deleted file mode 100644
index 9993558a..00000000
--- a/test/fail_histogram_dynamic_bin_2_test.cpp
+++ /dev/null
@@ -1,9 +0,0 @@
-#include <boost/histogram.hpp>
-#include <utility>
-
-using namespace boost::histogram;
-int main() {
-  auto h =
-      make_dynamic_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(std::make_pair(-2, 0));
-}
diff --git a/test/fail_histogram_dynamic_bin_3_test.cpp b/test/fail_histogram_dynamic_bin_3_test.cpp
deleted file mode 100644
index 26a5f896..00000000
--- a/test/fail_histogram_dynamic_bin_3_test.cpp
+++ /dev/null
@@ -1,9 +0,0 @@
-#include <boost/histogram.hpp>
-#include <vector>
-
-using namespace boost::histogram;
-int main() {
-  auto h =
-      make_dynamic_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(std::vector<int>({-2, 0}));
-}
diff --git a/test/fail_histogram_dynamic_bin_out_of_bounds_test.cpp b/test/fail_histogram_dynamic_bin_out_of_bounds_test.cpp
deleted file mode 100644
index 19f27899..00000000
--- a/test/fail_histogram_dynamic_bin_out_of_bounds_test.cpp
+++ /dev/null
@@ -1,7 +0,0 @@
-#include <boost/histogram.hpp>
-
-using namespace boost::histogram;
-int main() {
-  auto h = make_dynamic_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(0, -2);
-}
diff --git a/test/fail_histogram_dynamic_bin_tuple_out_of_bounds_test.cpp b/test/fail_histogram_dynamic_bin_tuple_out_of_bounds_test.cpp
deleted file mode 100644
index af06b291..00000000
--- a/test/fail_histogram_dynamic_bin_tuple_out_of_bounds_test.cpp
+++ /dev/null
@@ -1,8 +0,0 @@
-#include <boost/histogram.hpp>
-#include <tuple>
-
-using namespace boost::histogram;
-int main() {
-  auto h = make_dynamic_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(std::make_tuple(0, -2));
-}
diff --git a/test/fail_histogram_dynamic_bin_vector_out_of_bounds_test.cpp b/test/fail_histogram_dynamic_bin_vector_out_of_bounds_test.cpp
deleted file mode 100644
index b527cdc1..00000000
--- a/test/fail_histogram_dynamic_bin_vector_out_of_bounds_test.cpp
+++ /dev/null
@@ -1,8 +0,0 @@
-#include <boost/histogram.hpp>
-#include <vector>
-
-using namespace boost::histogram;
-int main() {
-  auto h = make_dynamic_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(std::vector<int>({0, -2}));
-}
diff --git a/test/fail_histogram_static_bin_wrong_size_test.cpp b/test/fail_histogram_static_at_vector_wrong_dimension_test.cpp
similarity index 100%
rename from test/fail_histogram_static_bin_wrong_size_test.cpp
rename to test/fail_histogram_static_at_vector_wrong_dimension_test.cpp
diff --git a/test/fail_histogram_static_bin_out_of_bounds_test.cpp b/test/fail_histogram_static_bin_out_of_bounds_test.cpp
deleted file mode 100644
index ec10b4cc..00000000
--- a/test/fail_histogram_static_bin_out_of_bounds_test.cpp
+++ /dev/null
@@ -1,7 +0,0 @@
-#include <boost/histogram.hpp>
-
-using namespace boost::histogram;
-int main() {
-  auto h = make_static_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(0, -2);
-}
diff --git a/test/fail_histogram_static_bin_tuple_out_of_bounds_test.cpp b/test/fail_histogram_static_bin_tuple_out_of_bounds_test.cpp
deleted file mode 100644
index 2688272a..00000000
--- a/test/fail_histogram_static_bin_tuple_out_of_bounds_test.cpp
+++ /dev/null
@@ -1,8 +0,0 @@
-#include <boost/histogram.hpp>
-#include <tuple>
-
-using namespace boost::histogram;
-int main() {
-  auto h = make_static_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(std::make_tuple(0, -2));
-}
diff --git a/test/fail_histogram_static_bin_vector_out_of_bounds_test.cpp b/test/fail_histogram_static_bin_vector_out_of_bounds_test.cpp
deleted file mode 100644
index 082ac181..00000000
--- a/test/fail_histogram_static_bin_vector_out_of_bounds_test.cpp
+++ /dev/null
@@ -1,8 +0,0 @@
-#include <boost/histogram.hpp>
-#include <vector>
-
-using namespace boost::histogram;
-int main() {
-  auto h = make_static_histogram(axis::integer<>(0, 2), axis::integer<>(0, 2));
-  h.at(std::vector<int>(-2, 0));
-}
diff --git a/test/histogram_test.cpp b/test/histogram_test.cpp
index c6051195..dfa7be61 100644
--- a/test/histogram_test.cpp
+++ b/test/histogram_test.cpp
@@ -17,6 +17,7 @@
 #include <boost/histogram/storage/array_storage.hpp>
 #include <boost/histogram/storage/weight_counter.hpp>
 #include <sstream>
+#include <stdexcept>
 #include <tuple>
 #include <utility>
 #include <vector>
@@ -810,6 +811,14 @@ void run_tests() {
     BOOST_TEST_EQ(h[i].variance(), 5);
   }
 
+  // bad bin access
+  {
+    auto h = make(Tag(), axis::integer<>(0, 1), axis::integer<>(0, 1));
+    BOOST_TEST_THROWS(h.at(0, 2), std::out_of_range);
+    BOOST_TEST_THROWS(h.at(std::make_pair(2, 0)), std::out_of_range);
+    BOOST_TEST_THROWS(h.at(std::vector<int>({0, 2})), std::out_of_range);
+  }
+
   // pass histogram to function
   {
     auto h = make(Tag(), axis::integer<>(0, 3));