diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index 5a766d4..166cbd0 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -1052,28 +1052,47 @@
     std::array<common_iter, N> m_common_iterator;
 };
 
+// Populates the shape and number of dimensions for the set of buffers.  Returns true if the
+// broadcast is "trivial"--that is, has each buffer being either a singleton or a full-size,
+// C-contiguous storage buffer.
 template <size_t N>
-bool broadcast(const std::array<buffer_info, N>& buffers, size_t& ndim, std::vector<size_t>& shape) {
+bool broadcast(const std::array<buffer_info, N> &buffers, size_t &ndim, std::vector<size_t> &shape) {
     ndim = std::accumulate(buffers.begin(), buffers.end(), size_t(0), [](size_t res, const buffer_info& buf) {
         return std::max(res, buf.ndim);
     });
 
-    shape = std::vector<size_t>(ndim, 1);
+    shape.clear();
+    shape.resize(ndim, 1);
+
     bool trivial_broadcast = true;
     for (size_t i = 0; i < N; ++i) {
+        trivial_broadcast = trivial_broadcast && (buffers[i].size == 1 || buffers[i].ndim == ndim);
+        size_t expect_stride = buffers[i].itemsize;
         auto res_iter = shape.rbegin();
-        bool i_trivial_broadcast = (buffers[i].size == 1) || (buffers[i].ndim == ndim);
-        for (auto shape_iter = buffers[i].shape.rbegin();
-             shape_iter != buffers[i].shape.rend(); ++shape_iter, ++res_iter) {
+        auto stride_iter = buffers[i].strides.rbegin();
+        auto shape_iter = buffers[i].shape.rbegin();
+        while (shape_iter != buffers[i].shape.rend()) {
+            const auto &dim_size_in = *shape_iter;
+            auto &dim_size_out = *res_iter;
 
-            if (*res_iter == 1)
-                *res_iter = *shape_iter;
-            else if ((*shape_iter != 1) && (*res_iter != *shape_iter))
+            // Each input dimension can either be 1 or `n`, but `n` values must match across buffers
+            if (dim_size_out == 1)
+                dim_size_out = dim_size_in;
+            else if (dim_size_in != 1 && dim_size_in != dim_size_out)
                 pybind11_fail("pybind11::vectorize: incompatible size/dimension of inputs!");
 
-            i_trivial_broadcast = i_trivial_broadcast && (*res_iter == *shape_iter);
+            if (trivial_broadcast && buffers[i].size > 1) {
+                if (dim_size_in == dim_size_out && expect_stride == *stride_iter) {
+                    expect_stride *= dim_size_in;
+                    ++stride_iter;
+                } else {
+                    trivial_broadcast = false;
+                }
+            }
+
+            ++shape_iter;
+            ++res_iter;
         }
-        trivial_broadcast = trivial_broadcast && i_trivial_broadcast;
     }
     return trivial_broadcast;
 }
@@ -1081,18 +1100,17 @@
 template <typename Func, typename Return, typename... Args>
 struct vectorize_helper {
     typename std::remove_reference<Func>::type f;
+    static constexpr size_t N = sizeof...(Args);
 
     template <typename T>
     explicit vectorize_helper(T&&f) : f(std::forward<T>(f)) { }
 
-    object operator()(array_t<Args, array::c_style | array::forcecast>... args) {
-        return run(args..., make_index_sequence<sizeof...(Args)>());
+    object operator()(array_t<Args, array::forcecast>... args) {
+        return run(args..., make_index_sequence<N>());
     }
 
-    template <size_t ... Index> object run(array_t<Args, array::c_style | array::forcecast>&... args, index_sequence<Index...> index) {
+    template <size_t ... Index> object run(array_t<Args, array::forcecast>&... args, index_sequence<Index...> index) {
         /* Request buffers from all parameters */
-        const size_t N = sizeof...(Args);
-
         std::array<buffer_info, N> buffers {{ args.request()... }};
 
         /* Determine dimensions parameters of output array */
@@ -1112,27 +1130,24 @@
         }
 
         if (size == 1)
-            return cast(f(*((Args *) buffers[Index].ptr)...));
+            return cast(f(*reinterpret_cast<Args *>(buffers[Index].ptr)...));
 
-        array_t<Return> result(shape, strides);
+        array_t<Return, array::c_style> result(shape, strides);
         auto buf = result.request();
         auto output = (Return *) buf.ptr;
 
         if (trivial_broadcast) {
             /* Call the function */
-            for (size_t i = 0; i < size; ++i) {
-                output[i] = f((buffers[Index].size == 1
-                               ? *((Args *) buffers[Index].ptr)
-                               : ((Args *) buffers[Index].ptr)[i])...);
-            }
+            for (size_t i = 0; i < size; ++i)
+                output[i] = f((reinterpret_cast<Args *>(buffers[Index].ptr)[buffers[Index].size == 1 ? 0 : i])...);
         } else {
-            apply_broadcast<N, Index...>(buffers, buf, index);
+            apply_broadcast<Index...>(buffers, buf, index);
         }
 
         return result;
     }
 
-    template <size_t N, size_t... Index>
+    template <size_t... Index>
     void apply_broadcast(const std::array<buffer_info, N> &buffers,
                          buffer_info &output, index_sequence<Index...>) {
         using input_iterator = multi_array_iterator<N>;
diff --git a/tests/test_numpy_vectorize.cpp b/tests/test_numpy_vectorize.cpp
index 6d94db2..e5adff8 100644
--- a/tests/test_numpy_vectorize.cpp
+++ b/tests/test_numpy_vectorize.cpp
@@ -38,4 +38,17 @@
     m.def("selective_func", [](py::array_t<int, py::array::c_style>) { return "Int branch taken."; });
     m.def("selective_func", [](py::array_t<float, py::array::c_style>) { return "Float branch taken."; });
     m.def("selective_func", [](py::array_t<std::complex<float>, py::array::c_style>) { return "Complex float branch taken."; });
+
+
+    // Internal optimization test for whether the input is trivially broadcastable:
+    m.def("vectorized_is_trivial", [](
+                py::array_t<int, py::array::forcecast> arg1,
+                py::array_t<float, py::array::forcecast> arg2,
+                py::array_t<double, py::array::forcecast> arg3
+                ) {
+        size_t ndim;
+        std::vector<size_t> shape;
+        std::array<py::buffer_info, 3> buffers {{ arg1.request(), arg2.request(), arg3.request() }};
+        return py::detail::broadcast(buffers, ndim, shape);
+    });
 });
diff --git a/tests/test_numpy_vectorize.py b/tests/test_numpy_vectorize.py
index 271241c..9a8c6ab 100644
--- a/tests/test_numpy_vectorize.py
+++ b/tests/test_numpy_vectorize.py
@@ -57,6 +57,35 @@
             my_func(x:int=5, y:float=3, z:float=2)
             my_func(x:int=6, y:float=3, z:float=2)
         """
+        with capture:
+            a, b, c = np.array([[1, 2, 3], [4, 5, 6]], order='F'), np.array([[2], [3]]), 2
+            assert np.allclose(f(a, b, c), a * b * c)
+        assert capture == """
+            my_func(x:int=1, y:float=2, z:float=2)
+            my_func(x:int=2, y:float=2, z:float=2)
+            my_func(x:int=3, y:float=2, z:float=2)
+            my_func(x:int=4, y:float=3, z:float=2)
+            my_func(x:int=5, y:float=3, z:float=2)
+            my_func(x:int=6, y:float=3, z:float=2)
+        """
+        with capture:
+            a, b, c = np.array([[1, 2, 3], [4, 5, 6]])[::, ::2], np.array([[2], [3]]), 2
+            assert np.allclose(f(a, b, c), a * b * c)
+        assert capture == """
+            my_func(x:int=1, y:float=2, z:float=2)
+            my_func(x:int=3, y:float=2, z:float=2)
+            my_func(x:int=4, y:float=3, z:float=2)
+            my_func(x:int=6, y:float=3, z:float=2)
+        """
+        with capture:
+            a, b, c = np.array([[1, 2, 3], [4, 5, 6]], order='F')[::, ::2], np.array([[2], [3]]), 2
+            assert np.allclose(f(a, b, c), a * b * c)
+        assert capture == """
+            my_func(x:int=1, y:float=2, z:float=2)
+            my_func(x:int=3, y:float=2, z:float=2)
+            my_func(x:int=4, y:float=3, z:float=2)
+            my_func(x:int=6, y:float=3, z:float=2)
+        """
 
 
 def test_type_selection():
@@ -73,3 +102,32 @@
     assert doc(vectorized_func) == """
         vectorized_func(arg0: numpy.ndarray[int32], arg1: numpy.ndarray[float32], arg2: numpy.ndarray[float64]) -> object
     """  # noqa: E501 line too long
+
+
+def test_trivial_broadcasting():
+    from pybind11_tests import vectorized_is_trivial
+
+    assert vectorized_is_trivial(1, 2, 3)
+    assert vectorized_is_trivial(np.array(1), np.array(2), 3)
+    assert vectorized_is_trivial(np.array([1, 3]), np.array([2, 4]), 3)
+    assert vectorized_is_trivial(
+        np.array([[1, 3, 5], [7, 9, 11]]), np.array([[2, 4, 6], [8, 10, 12]]), 3)
+    assert not vectorized_is_trivial(
+        np.array([[1, 2, 3], [4, 5, 6]]), np.array([2, 3, 4]), 2)
+    assert not vectorized_is_trivial(
+        np.array([[1, 2, 3], [4, 5, 6]]), np.array([[2], [3]]), 2)
+    z1 = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], dtype='int32')
+    z2 = np.array(z1, dtype='float32')
+    z3 = np.array(z1, dtype='float64')
+    assert vectorized_is_trivial(z1, z2, z3)
+    assert not vectorized_is_trivial(z1[::2, ::2], 1, 1)
+    assert vectorized_is_trivial(1, 1, z1[::2, ::2])
+    assert not vectorized_is_trivial(1, 1, z3[::2, ::2])
+    assert vectorized_is_trivial(z1, 1, z3[1::4, 1::4])
+
+    y1 = np.array(z1, order='F')
+    y2 = np.array(y1)
+    y3 = np.array(y1)
+    assert not vectorized_is_trivial(y1, y2, y3)
+    assert not vectorized_is_trivial(y1, z2, z3)
+    assert not vectorized_is_trivial(y1, 1, 1)