diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md
index bf20f7f7..91839552 100644
--- a/docs/CHANGELOG.md
+++ b/docs/CHANGELOG.md
@@ -3,10 +3,12 @@
 ## UPCOMING
 
 * Fix scaling a weighted storage [#559][]
+* Fix partial summation over a Categorical axis [#564][]
 * Support running type checking from Python < 3.8 [#542][]
 
 [#542]: https://github.com/scikit-hep/boost-histogram/pull/542
 [#559]: https://github.com/scikit-hep/boost-histogram/pull/559
+[#564]: https://github.com/scikit-hep/boost-histogram/pull/564
 
 ## Version 1.0
 
diff --git a/src/boost_histogram/_internal/axis.py b/src/boost_histogram/_internal/axis.py
index f109eb07..d88113af 100644
--- a/src/boost_histogram/_internal/axis.py
+++ b/src/boost_histogram/_internal/axis.py
@@ -165,15 +165,23 @@ def _process_loc(
         Compute start and stop into actual start and stop values in Boost.Histogram.
         None -> -1 or 0 for start, -> len or len+1 for stop. If start or stop are
         callable, then call them with the axes.
+
+        For a non-ordered axes, flow is all or nothing, so this will ensure overflow
+        is turned off if underflow is not None.
         """
 
         def _process_internal(item: Optional[AxCallOrInt], default: int) -> int:
             return default if item is None else item(self) if callable(item) else item
 
-        begin = _process_internal(start, -1 if self._ax.traits_underflow else 0)
-        end = _process_internal(
-            stop, len(self) + (1 if self._ax.traits_overflow else 0)
-        )
+        underflow = -1 if self._ax.traits_underflow else 0
+        overflow = 1 if self._ax.traits_overflow else 0
+
+        # Non-ordered axes only use flow if integrating from None to None
+        if not self._ax.traits_ordered and not (start is None and stop is None):
+            overflow = 0
+
+        begin = _process_internal(start, underflow)
+        end = _process_internal(stop, len(self) + overflow)
 
         return begin, end
 
diff --git a/src/register_algorithm.cpp b/src/register_algorithm.cpp
index ed339b86..fbf2e6d8 100644
--- a/src/register_algorithm.cpp
+++ b/src/register_algorithm.cpp
@@ -31,7 +31,7 @@ void register_algorithms(py::module& algorithm) {
                                 self.begin.index,
                                 self.end.index,
                                 merge,
-                                self.crop);
+                                self.crop ? "slice_mode.crop" : "slice_mode.shrink");
                 } else {
                     return py::
                         str("reduce_command(shrink{0}({1}, lower={2}, upper={3}{4}))")
diff --git a/tests/test_histogram_indexing.py b/tests/test_histogram_indexing.py
index bb24f0b5..3429b9fb 100644
--- a/tests/test_histogram_indexing.py
+++ b/tests/test_histogram_indexing.py
@@ -377,3 +377,30 @@ def test_axes_tuple_Nd():
 
     assert b1.ndim == 3
     assert a1.ndim == 2
+
+
+# issue 556
+def test_single_flow_bin():
+    # Flow is removed for category axes unless full sum is used
+    h = bh.Histogram(bh.axis.IntCategory([0, 1, 2]))
+    h.view(True)[:] = 1
+
+    assert h[::sum] == 4
+    assert h[0::sum] == 3
+    assert h[1::sum] == 2
+    assert h[2::sum] == 1
+    with pytest.raises(ValueError):
+        h[3::sum]
+
+    assert h[1:2][sum] == 4
+
+    h = bh.Histogram(bh.axis.Integer(0, 3))
+    h.view(True)[:] = 1
+
+    assert h[::sum] == 5
+    assert h[0::sum] == 4
+    assert h[1::sum] == 3
+    assert h[2::sum] == 2
+    assert h[3::sum] == 1
+
+    assert h[1:2][sum] == 5