diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index a0441efa3..e67d37151 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -14,6 +14,7 @@
 #include <numeric>
 #include <algorithm>
 #include <array>
+#include <cstdint>
 #include <cstdlib>
 #include <cstring>
 #include <sstream>
@@ -108,6 +109,18 @@ inline numpy_internals& get_numpy_internals() {
     return *ptr;
 }
 
+template <typename T> struct same_size {
+    template <typename U> using as = bool_constant<sizeof(T) == sizeof(U)>;
+};
+
+// Lookup a type according to its size, and return a value corresponding to the NumPy typenum.
+template <typename Concrete, typename... Check, typename... Int>
+constexpr int platform_lookup(Int... codes) {
+    using code_index = std::integral_constant<int, constexpr_first<same_size<Concrete>::template as, Check...>()>;
+    static_assert(code_index::value != sizeof...(Check), "Unable to match type on this platform");
+    return std::get<code_index::value>(std::make_tuple(codes...));
+}
+
 struct npy_api {
     enum constants {
         NPY_ARRAY_C_CONTIGUOUS_ = 0x0001,
@@ -126,7 +139,23 @@ struct npy_api {
         NPY_FLOAT_, NPY_DOUBLE_, NPY_LONGDOUBLE_,
         NPY_CFLOAT_, NPY_CDOUBLE_, NPY_CLONGDOUBLE_,
         NPY_OBJECT_ = 17,
-        NPY_STRING_, NPY_UNICODE_, NPY_VOID_
+        NPY_STRING_, NPY_UNICODE_, NPY_VOID_,
+        // Platform-dependent normalization
+        NPY_INT8_ = NPY_BYTE_,
+        NPY_UINT8_ = NPY_UBYTE_,
+        NPY_INT16_ = NPY_SHORT_,
+        NPY_UINT16_ = NPY_USHORT_,
+        // `npy_common.h` defines the integer aliases. In order, it checks:
+        // NPY_BITSOF_LONG, NPY_BITSOF_LONGLONG, NPY_BITSOF_INT, NPY_BITSOF_SHORT, NPY_BITSOF_CHAR
+        // and assigns the alias to the first matching size, so we should check in this order.
+        NPY_INT32_ = platform_lookup<std::int32_t, long, int, short>(
+            NPY_LONG_, NPY_INT_, NPY_SHORT_),
+        NPY_UINT32_ = platform_lookup<std::uint32_t, unsigned long, unsigned int, unsigned short>(
+            NPY_ULONG_, NPY_UINT_, NPY_USHORT_),
+        NPY_INT64_ = platform_lookup<std::int64_t, long, long long, int>(
+            NPY_LONG_, NPY_LONGLONG_, NPY_INT_),
+        NPY_UINT64_ = platform_lookup<std::uint64_t, unsigned long, unsigned long long, unsigned int>(
+            NPY_ULONG_, NPY_ULONGLONG_, NPY_UINT_),
     };
 
     typedef struct {
@@ -1004,8 +1033,8 @@ private:
     // NB: the order here must match the one in common.h
     constexpr static const int values[15] = {
         npy_api::NPY_BOOL_,
-        npy_api::NPY_BYTE_,   npy_api::NPY_UBYTE_,   npy_api::NPY_SHORT_,    npy_api::NPY_USHORT_,
-        npy_api::NPY_INT_,    npy_api::NPY_UINT_,    npy_api::NPY_LONGLONG_, npy_api::NPY_ULONGLONG_,
+        npy_api::NPY_BYTE_,   npy_api::NPY_UBYTE_,   npy_api::NPY_INT16_,    npy_api::NPY_UINT16_,
+        npy_api::NPY_INT32_,  npy_api::NPY_UINT32_,  npy_api::NPY_INT64_,    npy_api::NPY_UINT64_,
         npy_api::NPY_FLOAT_,  npy_api::NPY_DOUBLE_,  npy_api::NPY_LONGDOUBLE_,
         npy_api::NPY_CFLOAT_, npy_api::NPY_CDOUBLE_, npy_api::NPY_CLONGDOUBLE_
     };