diff --git a/gmp.c b/gmp.c
index 0e4737e0..1214a26e 100644
--- a/gmp.c
+++ b/gmp.c
@@ -7,21 +7,24 @@
 #include <stdlib.h>
 #include <string.h>
 
-#if !defined(PYPY_VERSION)
-#  define MAX_CACHE_SIZE 100
-#else
-#  define MAX_CACHE_SIZE 0
+#define ON_CPYTHON 1
+#if defined(PYPY_VERSION) || defined(GRAALVM_PYTHON)
+#  undef ON_CPYTHON
 #endif
-#define MAX_CACHED_SIZEOF 256
+
+#ifdef ON_CPYTHON
+#  define MAX_FREELIST_SIZE 100
+#  define MAX_FREELIST_SIZEOF 256
 
 typedef struct {
-    MPZ_Object *gmp_cache[MAX_CACHE_SIZE + 1];
-    size_t gmp_cache_size;
+    MPZ_Object *freelist[MAX_FREELIST_SIZE + 1];
+    size_t freelist_size;
 } gmp_global;
 
 _Thread_local gmp_global global = {
-    .gmp_cache_size = 0,
+    .freelist_size = 0,
 };
+#endif
 
 uint8_t bits_per_digit;
 Py_hash_t pyhash_modulus;
@@ -31,12 +34,14 @@ MPZ_new(void)
 {
     MPZ_Object *res;
 
-    if (global.gmp_cache_size) {
-        res = global.gmp_cache[--global.gmp_cache_size];
+#ifdef ON_CPYTHON
+    if (global.freelist_size) {
+        res = global.freelist[--global.freelist_size];
         (void)zz_set(0, &res->z);
-        Py_XINCREF((PyObject *)res);
+        Py_INCREF((PyObject *)res);
     }
     else {
+#endif
         res = PyObject_New(MPZ_Object, &MPZ_Type);
         if (!res) {
             return NULL; /* LCOV_EXCL_LINE */
@@ -44,7 +49,9 @@ MPZ_new(void)
         if (zz_init(&res->z)) {
             return (MPZ_Object *)PyErr_NoMemory(); /* LCOV_EXCL_LINE */
         }
+#ifdef ON_CPYTHON
     }
+#endif
     res->hash_cache = -1;
     return res;
 }
@@ -644,13 +651,15 @@ dealloc(PyObject *self)
 {
     MPZ_Object *u = (MPZ_Object *)self;
 
-    if (global.gmp_cache_size < MAX_CACHE_SIZE
-        && zz_sizeof(&u->z) <= MAX_CACHED_SIZEOF
+#ifdef ON_CPYTHON
+    if (global.freelist_size < MAX_FREELIST_SIZE
+        && zz_sizeof(&u->z) <= MAX_FREELIST_SIZEOF
         && MPZ_CheckExact(self))
     {
-        global.gmp_cache[global.gmp_cache_size++] = u;
+        global.freelist[global.freelist_size++] = u;
     }
     else {
+#endif
         freefunc tp_free;
 
         if (MPZ_CheckExact(self)) {
@@ -661,7 +670,9 @@ dealloc(PyObject *self)
         }
         zz_clear(&u->z);
         tp_free(self);
+#ifdef ON_CPYTHON
     }
+#endif
 }
 
 static PyObject *
@@ -2611,19 +2622,6 @@ gmp__mpmath_create(PyObject *self, PyObject *const *args, Py_ssize_t nargs)
     return Py_BuildValue("(bNNK)", negative, man, iexp, bc);
 }
 
-static PyObject *
-gmp__free_cache(PyObject *Py_UNUSED(module), PyObject *Py_UNUSED(args))
-{
-    while (global.gmp_cache_size) {
-        MPZ_Object *u = global.gmp_cache[--global.gmp_cache_size];
-        PyObject *self = (PyObject *)u;
-
-        zz_clear(&u->z);
-        PyObject_Free(self);
-    }
-    Py_RETURN_NONE;
-}
-
 static PyMethodDef gmp_functions[] = {
     {"gcd", (PyCFunction)gmp_gcd, METH_FASTCALL,
      ("gcd($module, /, *integers)\n--\n\n"
@@ -2656,8 +2654,6 @@ static PyMethodDef gmp_functions[] = {
     {"_mpmath_create", (PyCFunction)gmp__mpmath_create, METH_FASTCALL,
      ("_mpmath_create($module, man, exp, prec=0, rnd='d', /)\n--\n\n"
       "Helper function for mpmath.")},
-    {"_free_cache", gmp__free_cache, METH_NOARGS,
-     "_free_cache($module)\n--\n\nFree mpz's cache."},
     {NULL} /* sentinel */
 };
 
diff --git a/tests/test_mpz.py b/tests/test_mpz.py
index ab89ca49..146987a6 100644
--- a/tests/test_mpz.py
+++ b/tests/test_mpz.py
@@ -8,7 +8,6 @@
 import sys
 import warnings
 from concurrent.futures import ThreadPoolExecutor
-from subprocess import run
 
 import pytest
 from gmp import mpz
@@ -1093,10 +1092,3 @@ def test_int_api():
                 continue
         mz_sig = inspect.signature(mz)
         assert m_sig == mz_sig
-
-
-def test_mpz_clear():
-    # for coverage (test module cleanup)
-    res = run([sys.executable, "-c",
-               "import gmp; a = gmp.mpz(1); del a; gmp._free_cache()"])
-    assert res.returncode == 0