diff --git a/ci/environment-3.7.yml b/ci/environment-3.7.yml
index 355cfc8..64dca66 100644
--- a/ci/environment-3.7.yml
+++ b/ci/environment-3.7.yml
@@ -5,7 +5,7 @@ dependencies:
   - python=3.7
   - xarray
   - dask
-  - numpy=1.16
+  - numpy=1.17
   - pytest
   - pip
   - pip:
diff --git a/setup.py b/setup.py
index 4e6f771..d119cce 100644
--- a/setup.py
+++ b/setup.py
@@ -20,7 +20,7 @@
     "Topic :: Scientific/Engineering",
 ]
 
-INSTALL_REQUIRES = ["xarray>=0.12.0", "dask", "numpy>=1.16"]
+INSTALL_REQUIRES = ["xarray>=0.12.0", "dask", "numpy>=1.17"]
 PYTHON_REQUIRES = ">=3.7"
 
 DESCRIPTION = "Fast, flexible, label-aware histograms for numpy and xarray"
diff --git a/xhistogram/core.py b/xhistogram/core.py
index 97a1c7e..c13dda9 100644
--- a/xhistogram/core.py
+++ b/xhistogram/core.py
@@ -193,11 +193,7 @@ def _bincount_2d_vectorized(
 
 
 def _bincount(*all_arrays, weights=False, axis=None, bins=None, density=None):
-
-    # is this necessary?
-    all_arrays_broadcast = broadcast_arrays(*all_arrays)
-
-    a0 = all_arrays_broadcast[0]
+    a0 = all_arrays[0]
 
     do_full_array = (axis is None) or (set(axis) == set(_range(a0.ndim)))
 
@@ -226,7 +222,7 @@ def reshape_input(a):
             d = reshape(c, (new_dim_0, new_dim_1))
         return d
 
-    all_arrays_reshaped = [reshape_input(a) for a in all_arrays_broadcast]
+    all_arrays_reshaped = [reshape_input(a) for a in all_arrays]
 
     if weights:
         weights_array = all_arrays_reshaped.pop()
@@ -257,8 +253,8 @@ def histogram(
     Parameters
     ----------
     args : array_like
-        Input data. The number of input arguments determines the dimensonality
-        of the histogram. For example, two arguments prodocue a 2D histogram.
+        Input data. The number of input arguments determines the dimensionality
+        of the histogram. For example, two arguments produce a 2D histogram.
         All args must have the same size.
     bins :  int, str or numpy array or a list of ints, strs and/or arrays, optional
         If a list, there should be one entry for each item in ``args``.
@@ -358,21 +354,20 @@ def histogram(
 
     dtype = "i8" if not has_weights else weights.dtype
 
-    # here I am assuming all the arrays have the same shape
-    # probably needs to be generalized
-    input_indexes = [tuple(_range(a.ndim)) for a in all_arrays]
-    input_index = input_indexes[0]
-    assert all([ii == input_index for ii in input_indexes])
+    # Broadcast input arrays. Note that this dispatches to `dsa.broadcast_arrays` as necessary.
+    all_arrays = broadcast_arrays(*all_arrays)
+    # Since all arrays now have the same shape, just get the axes of the first.
+    input_axes = tuple(_range(all_arrays[0].ndim))
 
     # Some sanity checks and format bins and range correctly
     bins = _ensure_correctly_formatted_bins(bins, n_inputs)
     range = _ensure_correctly_formatted_range(range, n_inputs)
 
-    # histogram_bin_edges trigges computation on dask arrays. It would be possible
+    # histogram_bin_edges triggers computation on dask arrays. It would be possible
     # to write a version of this that doesn't trigger when `range` is provided, but
     # for now let's just use np.histogram_bin_edges
     if is_dask_array:
-        if not all([isinstance(b, np.ndarray) for b in bins]):
+        if not all(isinstance(b, np.ndarray) for b in bins):
             raise TypeError(
                 "When using dask arrays, bins must be provided as numpy array(s) of edges"
             )
@@ -382,11 +377,11 @@ def histogram(
         ]
     bincount_kwargs = dict(weights=has_weights, axis=axis, bins=bins, density=density)
 
-    # keep these axes in the inputs
+    # remove these axes from the inputs
     if axis is not None:
-        drop_axes = tuple([ii for ii in input_index if ii in axis])
+        drop_axes = tuple(axis)
     else:
-        drop_axes = input_index
+        drop_axes = input_axes
 
     if _any_dask_array(weights, *all_arrays):
         # We should be able to just apply the bin_count function to every
@@ -405,16 +400,14 @@ def histogram(
 
         adjust_chunks = {i: (lambda x: 1) for i in drop_axes}
 
-        new_axes = {
-            max(input_index) + 1 + i: axis_len
-            for i, axis_len in enumerate([len(bin) - 1 for bin in bins])
-        }
-        out_index = input_index + tuple(new_axes)
+        new_axes_start = max(input_axes) + 1
+        new_axes = {new_axes_start + i: len(bin) - 1 for i, bin in enumerate(bins)}
+        out_index = input_axes + tuple(new_axes)
 
         blockwise_args = []
         for arg in all_arrays:
             blockwise_args.append(arg)
-            blockwise_args.append(input_index)
+            blockwise_args.append(input_axes)
 
         bin_counts = dsa.blockwise(
             _bincount,
@@ -432,7 +425,7 @@ def histogram(
         bin_counts = _bincount(*all_arrays, **bincount_kwargs).squeeze(drop_axes)
 
     if density:
-        # Normalise by dividing by bin counts and areas such that all the
+        # Normalize by dividing by bin counts and areas such that all the
         # histogram data integrated over all dimensions = 1
         bin_widths = [np.diff(b) for b in bins]
         if n_inputs == 1:
diff --git a/xhistogram/test/test_core.py b/xhistogram/test/test_core.py
index e0df0ee..f6ebcc3 100644
--- a/xhistogram/test/test_core.py
+++ b/xhistogram/test/test_core.py
@@ -122,6 +122,34 @@ def test_histogram_results_2d():
     np.testing.assert_array_equal(hist, h)
 
 
+@pytest.mark.parametrize("dask", [False, True])
+def test_histogram_results_2d_broadcasting(dask):
+    nrows, ncols = 5, 20
+    data_a = np.random.randn(ncols)
+    data_b = np.random.randn(nrows, ncols)
+    nbins_a = 9
+    bins_a = np.linspace(-4, 4, nbins_a + 1)
+    nbins_b = 10
+    bins_b = np.linspace(-4, 4, nbins_b + 1)
+
+    if dask:
+        test_data_a = dsa.from_array(data_a, chunks=3)
+        test_data_b = dsa.from_array(data_b, chunks=(2, 7))
+    else:
+        test_data_a = data_a
+        test_data_b = data_b
+
+    h, _ = histogram(test_data_a, test_data_b, bins=[bins_a, bins_b])
+    assert h.shape == (nbins_a, nbins_b)
+
+    hist, _, _ = np.histogram2d(
+        np.broadcast_to(data_a, data_b.shape).ravel(),
+        data_b.ravel(),
+        bins=[bins_a, bins_b],
+    )
+    np.testing.assert_array_equal(hist, h)
+
+
 def test_histogram_results_2d_density():
     nrows, ncols = 5, 20
     data_a = np.random.randn(nrows, ncols)
@@ -228,7 +256,7 @@ def test_histogram_shape(use_dask, block_size):
 
 
 def test_histogram_dask():
-    """ Test that fails with dask arrays and inappropriate bins"""
+    """Test that fails with dask arrays and inappropriate bins"""
     shape = 10, 15, 12, 20
     b = empty_dask_array(shape, chunks=(1,) + shape[1:])
     histogram(b, bins=bins_arr)  # Should work when bins is all numpy arrays
@@ -255,7 +283,7 @@ def test_histogram_dask():
     ],
 )
 def test_ensure_correctly_formatted_bins(in_out):
-    """ Test the helper function _ensure_correctly_formatted_bins"""
+    """Test the helper function _ensure_correctly_formatted_bins"""
     bins_in, n, bins_expected = in_out
     if bins_expected is not None:
         bins = _ensure_correctly_formatted_bins(bins_in, n)
@@ -277,7 +305,7 @@ def test_ensure_correctly_formatted_bins(in_out):
     ],
 )
 def test_ensure_correctly_formatted_range(in_out):
-    """ Test the helper function _ensure_correctly_formatted_range"""
+    """Test the helper function _ensure_correctly_formatted_range"""
     range_in, n, range_expected = in_out
     if range_expected is not None:
         range_ = _ensure_correctly_formatted_range(range_in, n)