diff --git a/peps/pep-0757.rst b/peps/pep-0757.rst
index fd315a8db8d..1bd675b8b1a 100644
--- a/peps/pep-0757.rst
+++ b/peps/pep-0757.rst
@@ -110,9 +110,9 @@ Export a Python integer as a digits array::
 On CPython 3.14, no memory copy is needed, it's just a thin wrapper to
 expose Python int internal digits array.
 
-``PyLong_DigitArray._reserved`` stores a strong reference to the Python
-:class:`int` object to make sure that that structure remains valid until
-``PyLong_FreeExport()`` is called.
+``PyLong_DigitArray._reserved``, if ``digits`` not ``NULL``, stores a strong
+reference to the Python :class:`int` object to make sure that that structure
+remains valid until ``PyLong_FreeExport()`` is called.
 
 
 PyLong_Export()
@@ -136,8 +136,8 @@ Python :class:`int` object or a subclass.
 ``PyLong_FreeExport()`` must be called once done with using *array*.
 
 
-PyLong_FreeDigitArray()
-^^^^^^^^^^^^^^^^^^^^^^^
+PyLong_FreeExport()
+^^^^^^^^^^^^^^^^^^^
 
 API::
 
@@ -256,35 +256,35 @@ Code::
     static void
     mpz_set_PyLong(mpz_t z, PyObject *obj)
     {
-        int overflow;
-        long val = PyLong_AsLongAndOverflow(obj, &overflow);
-
-        if (overflow) {
-            const PyLongLayout* layout = PyLong_GetNativeLayout();
-            static PyLong_DigitArray long_export;
-
-            PyLong_Export(obj, &long_export);
-            if (long_export.digits) {
-                mpz_import(z, long_export.ndigits, layout->digits_order,
-                           layout->digit_size, layout->endian,
-                           layout->digit_size*8 - layout->bits_per_digit,
-                           long_export.digits);
-            }
-            else {
-                if (long_export.negative) {
-                    long_export.value = -long_export.value;
-                }
-                mpz_import(z, 1, -1, sizeof(int64_t), 0, 0,
-                           &long_export.value);
-            }
-            PyLong_FreeExport(&long_export);
-
+        const PyLongLayout* layout = PyLong_GetNativeLayout();
+        static PyLong_DigitArray long_export;
+
+        PyLong_Export(obj, &long_export);
+        if (long_export.digits) {
+            mpz_import(z, long_export.ndigits, layout->digits_order,
+                       layout->digit_size, layout->endian,
+                       layout->digit_size*8 - layout->bits_per_digit,
+                       long_export.digits);
             if (long_export.negative) {
                 mpz_neg(z, z);
             }
+            PyLong_FreeExport(&long_export);
         }
         else {
-            mpz_set_si(z, val);
+            if (LONG_MIN <= long_export.value <= LONG_MAX) {
+                mpz_set_si(z, long_export.value);
+            }
+            else {
+                mpz_import(z, 1, -1, sizeof(int64_t), 0, 0,
+                           &long_export.value);
+                if (long_export.value < 0) {
+                    mpz_t tmp;
+                    mpz_init(tmp);
+                    mpz_ui_pow_ui(tmp, 2, 8*sizeof(size_t));
+                    mpz_sub(z, z, tmp);
+                    mpz_clear(tmp);
+                }
+            }
         }
     }