diff --git a/tests/test_numpy_array.cpp b/tests/test_numpy_array.cpp
index cdf0b82df..156a3bfa8 100644
--- a/tests/test_numpy_array.cpp
+++ b/tests/test_numpy_array.cpp
@@ -14,6 +14,67 @@
 
 #include <cstdint>
 
+// Size / dtype checks.
+struct DtypeCheck {
+    py::dtype numpy{};
+    py::dtype pybind11{};
+};
+
+template <typename T>
+DtypeCheck get_dtype_check(const char* name) {
+    py::module np = py::module::import("numpy");
+    DtypeCheck check{};
+    check.numpy = np.attr("dtype")(np.attr(name));
+    check.pybind11 = py::dtype::of<T>();
+    return check;
+}
+
+std::vector<DtypeCheck> get_concrete_dtype_checks() {
+    return {
+        // Normalization
+        get_dtype_check<std::int8_t>("int8"),
+        get_dtype_check<std::uint8_t>("uint8"),
+        get_dtype_check<std::int16_t>("int16"),
+        get_dtype_check<std::uint16_t>("uint16"),
+        get_dtype_check<std::int32_t>("int32"),
+        get_dtype_check<std::uint32_t>("uint32"),
+        get_dtype_check<std::int64_t>("int64"),
+        get_dtype_check<std::uint64_t>("uint64")
+    };
+}
+
+struct DtypeSizeCheck {
+    std::string name{};
+    int size_cpp{};
+    int size_numpy{};
+    // For debugging.
+    py::dtype dtype{};
+};
+
+template <typename T>
+DtypeSizeCheck get_dtype_size_check() {
+    DtypeSizeCheck check{};
+    check.name = py::type_id<T>();
+    check.size_cpp = sizeof(T);
+    check.dtype = py::dtype::of<T>();
+    check.size_numpy = check.dtype.attr("itemsize").template cast<int>();
+    return check;
+}
+
+std::vector<DtypeSizeCheck> get_platform_dtype_size_checks() {
+    return {
+        get_dtype_size_check<short>(),
+        get_dtype_size_check<unsigned short>(),
+        get_dtype_size_check<int>(),
+        get_dtype_size_check<unsigned int>(),
+        get_dtype_size_check<long>(),
+        get_dtype_size_check<unsigned long>(),
+        get_dtype_size_check<long long>(),
+        get_dtype_size_check<unsigned long long>(),
+    };
+}
+
+// Arrays.
 using arr = py::array;
 using arr_t = py::array_t<uint16_t, 0>;
 static_assert(std::is_same<arr_t::value_type, uint16_t>::value, "");
@@ -75,6 +136,26 @@ TEST_SUBMODULE(numpy_array, sm) {
     try { py::module::import("numpy"); }
     catch (...) { return; }
 
+    // test_dtypes
+    py::class_<DtypeCheck>(sm, "DtypeCheck")
+        .def_readonly("numpy", &DtypeCheck::numpy)
+        .def_readonly("pybind11", &DtypeCheck::pybind11)
+        .def("__repr__", [](const DtypeCheck& self) {
+            return py::str("<DtypeCheck numpy={} pybind11={}>").format(
+                self.numpy, self.pybind11);
+        });
+    sm.def("get_concrete_dtype_checks", &get_concrete_dtype_checks);
+
+    py::class_<DtypeSizeCheck>(sm, "DtypeSizeCheck")
+        .def_readonly("name", &DtypeSizeCheck::name)
+        .def_readonly("size_cpp", &DtypeSizeCheck::size_cpp)
+        .def_readonly("size_numpy", &DtypeSizeCheck::size_numpy)
+        .def("__repr__", [](const DtypeSizeCheck& self) {
+            return py::str("<DtypeSizeCheck name='{}' size_cpp={} size_numpy={} dtype={}>").format(
+                self.name, self.size_cpp, self.size_numpy, self.dtype);
+        });
+    sm.def("get_platform_dtype_size_checks", &get_platform_dtype_size_checks);
+
     // test_array_attributes
     sm.def("ndim", [](const arr& a) { return a.ndim(); });
     sm.def("shape", [](const arr& a) { return arr(a.ndim(), a.shape()); });
diff --git a/tests/test_numpy_array.py b/tests/test_numpy_array.py
index 8bacb7f6d..17c87ef7b 100644
--- a/tests/test_numpy_array.py
+++ b/tests/test_numpy_array.py
@@ -7,6 +7,21 @@ with pytest.suppress(ImportError):
     import numpy as np
 
 
+def test_dtypes():
+    # See issue #1328.
+    # - Platform-dependent sizes.
+    for size_check in m.get_platform_dtype_size_checks():
+        print(size_check)
+        assert size_check.size_cpp == size_check.size_numpy, size_check
+    # - Concrete sizes.
+    for check in m.get_concrete_dtype_checks():
+        print(check)
+        assert check.numpy == check.pybind11, check
+        if check.numpy.num != check.pybind11.num:
+            print("NOTE: typenum mismatch for {}: {} != {}".format(
+                check, check.numpy.num, check.pybind11.num))
+
+
 @pytest.fixture(scope='function')
 def arr():
     return np.array([[1, 2, 3], [4, 5, 6]], '=u2')