diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 50f69377523818..352112eb98344d 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -180,6 +180,43 @@ _Py_bit_length(unsigned long x)
 }
 
 
+static inline int
+_Py_bit_length64(uint64_t x)
+{
+#if (defined(__clang__) || defined(__GNUC__))
+    if (x != 0) {
+        // __builtin_clzll() is available since GCC 3.4.
+        // Undefined behavior for x == 0.
+        return (int)sizeof(uint64_t) * 8 - __builtin_clzll(x);
+    }
+    else {
+        return 0;
+    }
+#elif defined(_MSC_VER) && defined(_WIN64)
+    // _BitScanReverse64() is documented to search 64 bits.
+    unsigned long msb;
+    if (_BitScanReverse64(&msb, x)) {
+        return (int)msb + 1;
+    }
+    else {
+        return 0;
+    }
+#else
+    const int BIT_LENGTH_TABLE[32] = {
+        0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
+        5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
+    };
+    int msb = 0;
+    while (x >= 32) {
+        msb += 6;
+        x >>= 6;
+    }
+    msb += BIT_LENGTH_TABLE[x];
+    return msb;
+#endif
+}
+
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/Modules/_heapqmodule.c b/Modules/_heapqmodule.c
index 80fe9cff98509d..3d7434ddaa5626 100644
--- a/Modules/_heapqmodule.c
+++ b/Modules/_heapqmodule.c
@@ -12,6 +12,7 @@ annotated by François Pinard, and converted to C by Raymond Hettinger.
 
 #include "Python.h"
 #include "pycore_list.h"          // _PyList_ITEMS()
+#include "pycore_bitutils.h"      // _Py_bit_length(), _Py_bit_length64()
 
 #include "clinic/_heapqmodule.c.h"
 
@@ -279,16 +280,15 @@ _heapq_heappushpop_impl(PyObject *module, PyObject *heap, PyObject *item)
     return returnitem;
 }
 
-static Py_ssize_t
+static inline Py_ssize_t
 keep_top_bit(Py_ssize_t n)
 {
-    int i = 0;
-
-    while (n > 1) {
-        n >>= 1;
-        i++;
-    }
-    return n << i;
+    Py_BUILD_ASSERT(sizeof(Py_ssize_t) <= sizeof(uint64_t));
+#if defined(SIZEOF_SIZE_T) && SIZEOF_SIZE_T <= 4
+    return (Py_ssize_t)1 << (_Py_bit_length((unsigned long)n) - 1);
+#else
+    return (Py_ssize_t)1 << (_Py_bit_length64((uint64_t)n) - 1);
+#endif
 }
 
 /* Cache friendly version of heapify()
diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index 0451688a46c75f..235f4755f66c41 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -227,6 +227,47 @@ test_bit_length(PyObject *self, PyObject *Py_UNUSED(args))
 }
 
 
+static int
+check_bit_length64(uint64_t x, int expected)
+{
+    // Use volatile to prevent the compiler to optimize out the whole test
+    volatile uint64_t u = x;
+    int len = _Py_bit_length64(u);
+    if (len != expected) {
+        PyErr_Format(PyExc_AssertionError,
+                     "_Py_bit_length(%lu) returns %i, expected %i",
+                     x, len, expected);
+        return -1;
+    }
+    return 0;
+}
+
+
+static PyObject*
+test_bit_length64(PyObject *self, PyObject *Py_UNUSED(args))
+{
+#define CHECK(X, RESULT) \
+    do { \
+        if (check_bit_length64(X, RESULT) < 0) { \
+            return NULL; \
+        } \
+    } while (0)
+
+    CHECK(0, 0);
+    CHECK(1, 1);
+    CHECK(0x1000, 13);
+    CHECK(0x1234, 13);
+    CHECK(0x54321, 19);
+    CHECK(0x7FFFFFFF, 31);
+    CHECK(0xFFFFFFFF, 32);
+    CHECK(0x7FFFFFFFFFFFFFFFULL, 63);
+    CHECK(0xFFFFFFFFFFFFFFFFULL, 64);
+    Py_RETURN_NONE;
+
+#undef CHECK
+}
+
+
 #define TO_PTR(ch) ((void*)(uintptr_t)ch)
 #define FROM_PTR(ptr) ((uintptr_t)ptr)
 #define VALUE(key) (1 + ((int)(key) - 'a'))
@@ -2056,6 +2097,7 @@ static PyMethodDef module_functions[] = {
     {"test_bswap", test_bswap, METH_NOARGS},
     {"test_popcount", test_popcount, METH_NOARGS},
     {"test_bit_length", test_bit_length, METH_NOARGS},
+    {"test_bit_length64", test_bit_length64, METH_NOARGS},
     {"test_hashtable", test_hashtable, METH_NOARGS},
     {"get_config", test_get_config, METH_NOARGS},
     {"set_config", test_set_config, METH_O},