diff --git a/include/boost/histogram/algorithm/reduce.hpp b/include/boost/histogram/algorithm/reduce.hpp
index eff3a5b0..8340c25b 100644
--- a/include/boost/histogram/algorithm/reduce.hpp
+++ b/include/boost/histogram/algorithm/reduce.hpp
@@ -25,15 +25,14 @@ namespace algorithm {
 
 struct reduce_option_type {
   unsigned iaxis = 0;
-  bool has_range = false;
   double lower, upper;
   unsigned merge = 0;
 
   reduce_option_type() noexcept = default;
 
-  reduce_option_type(unsigned i, bool b, double l, double u, unsigned m)
-      : iaxis(i), has_range(b), lower(l), upper(u), merge(m) {
-    if (has_range && l == u) throw std::invalid_argument("lower != upper required");
+  reduce_option_type(unsigned i, double l, double u, unsigned m)
+      : iaxis(i), lower(l), upper(u), merge(m) {
+    if (lower == upper) throw std::invalid_argument("lower != upper required");
     if (merge == 0) throw std::invalid_argument("merge > 0 required");
   }
 
@@ -41,16 +40,17 @@ struct reduce_option_type {
 };
 
 reduce_option_type shrink(unsigned iaxis, double lower, double upper) {
-  return {iaxis, true, lower, upper, 1};
+  return {iaxis, lower, upper, 1};
 }
 
 reduce_option_type shrink_and_rebin(unsigned iaxis, double lower, double upper,
                                     unsigned merge) {
-  return {iaxis, true, lower, upper, merge};
+  return {iaxis, lower, upper, merge};
 }
 
 reduce_option_type rebin(unsigned iaxis, unsigned merge) {
-  return {iaxis, false, 0.0, 0.0, merge};
+  return {iaxis, std::numeric_limits<double>::quiet_NaN(),
+          std::numeric_limits<double>::quiet_NaN(), merge};
 }
 
 template <typename A, typename S, typename C, typename = detail::requires_iterable<C>>
@@ -100,7 +100,8 @@ histogram<A, S> reduce(const histogram<A, S>& h, const C& c) {
       if (opt.lower < opt.upper) {
         while (begin != end && a.value(begin) < opt.lower) ++begin;
         while (end != begin && a.value(end - 1) >= opt.upper) --end;
-      } else if (opt.upper < opt.lower) {
+      } else if (opt.lower > opt.upper) {
+        // for inverted axis::regular
         while (begin != end && a.value(begin) > opt.lower) ++begin;
         while (end != begin && a.value(end - 1) <= opt.upper) --end;
       }
diff --git a/include/boost/histogram/axis/circular.hpp b/include/boost/histogram/axis/circular.hpp
index dc70158f..775e50f1 100644
--- a/include/boost/histogram/axis/circular.hpp
+++ b/include/boost/histogram/axis/circular.hpp
@@ -57,6 +57,15 @@ public:
       throw std::invalid_argument("invalid phase or perimeter");
   }
 
+  /// Constructor used by algorithm::reduce to shrink and rebin (not for users).
+  circular(const circular& src, unsigned begin, unsigned end, unsigned merge)
+      : base_type(src.size() / merge, src.metadata(), src.options())
+      , phase_(src.phase_)
+      , delta_(src.delta_ * merge) {
+    if (!(begin == 0 && end == src.size()))
+      throw std::invalid_argument("cannot shrink circular axis");
+  }
+
   circular() = default;
 
   /// Returns the bin index for the passed argument.
diff --git a/test/algorithm_reduce_test.cpp b/test/algorithm_reduce_test.cpp
index fa5575bc..bb75dd84 100644
--- a/test/algorithm_reduce_test.cpp
+++ b/test/algorithm_reduce_test.cpp
@@ -7,8 +7,12 @@
 #include <boost/core/lightweight_test.hpp>
 #include <boost/histogram/algorithm/reduce.hpp>
 #include <boost/histogram/algorithm/sum.hpp>
+#include <boost/histogram/axis/category.hpp>
+#include <boost/histogram/axis/circular.hpp>
+#include <boost/histogram/axis/integer.hpp>
 #include <boost/histogram/axis/ostream_operators.hpp>
 #include <boost/histogram/axis/regular.hpp>
+#include <boost/histogram/axis/variable.hpp>
 #include <boost/histogram/ostream_operators.hpp>
 #include <vector>
 #include "utility_histogram.hpp"
@@ -116,6 +120,17 @@ void run_tests() {
     BOOST_TEST_THROWS(reduce(h, rebin(0, 2)), std::invalid_argument);
   }
 
+  // reduce on circular axis, shrink must fail, also rebin with remainder
+  {
+    auto h = make(Tag(), axis::circular<>(4, 1, 4));
+    BOOST_TEST_THROWS(reduce(h, shrink(0, 0, 2)), std::invalid_argument);
+    BOOST_TEST_THROWS(reduce(h, rebin(0, 3)), std::invalid_argument);
+    auto hr = reduce(h, rebin(0, 2));
+    BOOST_TEST_EQ(hr.axis().size(), 2);
+    BOOST_TEST_EQ(hr.axis()[0].lower(), 1);
+    BOOST_TEST_EQ(hr.axis()[1].upper(), 5);
+  }
+
   // reduce on axis with inverted range
   {
     auto h = make(Tag(), regular(4, 2, -2));
diff --git a/test/axis_circular_test.cpp b/test/axis_circular_test.cpp
index ff0dc2d3..792ea0a1 100644
--- a/test/axis_circular_test.cpp
+++ b/test/axis_circular_test.cpp
@@ -49,5 +49,17 @@ int main() {
   // iterators
   { test_axis_iterator(axis::circular<>(5, 0, 1, ""), 0, 5); }
 
+  // shrink and rebin
+  {
+    using A = axis::circular<>;
+    auto a = A(4, 1, 4);
+    BOOST_TEST_THROWS(A(a, 1, 4, 1), std::invalid_argument);
+    BOOST_TEST_THROWS(A(a, 0, 3, 1), std::invalid_argument);
+    auto b = A(a, 0, 4, 2);
+    BOOST_TEST_EQ(b.size(), 2);
+    BOOST_TEST_EQ(b.value(0), 1);
+    BOOST_TEST_EQ(b.value(2), 5);
+  }
+
   return boost::report_errors();
 }