diff --git a/gmp.c b/gmp.c
index 9485fd03..cde6eeeb 100644
--- a/gmp.c
+++ b/gmp.c
@@ -33,7 +33,6 @@ MPZ_new(void)
     if (global.freelist_size) {
         res = global.freelist[--global.freelist_size];
         (void)zz_set(0, &res->z);
-        Py_INCREF((PyObject *)res);
     }
     else {
 #endif
@@ -607,16 +606,28 @@ new(PyTypeObject *type, PyObject *args, PyObject *keywds)
     return new_impl(type, arg, base);
 }
 
+#ifdef ON_CPYTHON
 static void
-dealloc(PyObject *self)
+finalize(PyObject *self)
 {
     MPZ_Object *u = (MPZ_Object *)self;
 
-#ifdef ON_CPYTHON
     if (global.freelist_size < MAX_FREELIST_SIZE
         && zz_sizeof(&u->z) <= MAX_FREELIST_SIZEOF
         && MPZ_CheckExact(self))
     {
+        Py_INCREF(self);
+    }
+}
+#endif
+
+static void
+dealloc(PyObject *self)
+{
+    MPZ_Object *u = (MPZ_Object *)self;
+
+#ifdef ON_CPYTHON
+    if (PyObject_CallFinalizerFromDealloc(self)) {
         global.freelist[global.freelist_size++] = u;
     }
     else {
@@ -1949,6 +1960,9 @@ PyTypeObject MPZ_Type = {
     .tp_basicsize = sizeof(MPZ_Object),
     .tp_new = new,
     .tp_dealloc = dealloc,
+#ifdef ON_CPYTHON
+    .tp_finalize = finalize,
+#endif
     .tp_repr = repr,
     .tp_str = str,
     .tp_richcompare = richcompare,