diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index b115f67f228ba7..f59f9a76abd5ea 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -221,6 +221,8 @@ typedef struct
     PyThread_type_lock lock;
 } compobject;
 
+#define _compobject_CAST(op)    ((compobject *)op)
+
 static void
 zlib_error(zlibstate *state, z_stream zst, int err, const char *msg)
 {
@@ -261,7 +263,9 @@ static compobject *
 newcompobject(PyTypeObject *type)
 {
     compobject *self;
-    self = PyObject_New(compobject, type);
+    assert(type != NULL);
+    assert(type->tp_alloc != NULL);
+    self = _compobject_CAST(type->tp_alloc(type, 0));
     if (self == NULL)
         return NULL;
     self->eof = 0;
@@ -704,31 +708,41 @@ zlib_decompressobj_impl(PyObject *module, int wbits, PyObject *zdict)
 }
 
 static void
-Dealloc(compobject *self)
+compobject_dealloc_impl(PyObject *op, int (*dealloc)(z_streamp))
 {
-    PyObject *type = (PyObject *)Py_TYPE(self);
+    PyTypeObject *type = Py_TYPE(op);
+    PyObject_GC_UnTrack(op);
+    compobject *self = _compobject_CAST(op);
+    if (self->is_initialised) {
+        (void)dealloc(&self->zst);
+    }
     PyThread_free_lock(self->lock);
     Py_XDECREF(self->unused_data);
     Py_XDECREF(self->unconsumed_tail);
     Py_XDECREF(self->zdict);
-    PyObject_Free(self);
+    type->tp_free(self);
     Py_DECREF(type);
 }
 
+static int
+compobject_traverse(PyObject *op, visitproc visit, void *arg)
+{
+    compobject *self = _compobject_CAST(op);
+    Py_VISIT(Py_TYPE(op));
+    Py_VISIT(self->zdict);
+    return 0;
+}
+
 static void
-Comp_dealloc(compobject *self)
+Comp_dealloc(PyObject *op)
 {
-    if (self->is_initialised)
-        deflateEnd(&self->zst);
-    Dealloc(self);
+    compobject_dealloc_impl(op, &deflateEnd);
 }
 
 static void
-Decomp_dealloc(compobject *self)
+Decomp_dealloc(PyObject *op)
 {
-    if (self->is_initialised)
-        inflateEnd(&self->zst);
-    Dealloc(self);
+    compobject_dealloc_impl(op, &inflateEnd);
 }
 
 /*[clinic input]
@@ -1353,15 +1367,19 @@ typedef struct {
     char needs_input;
 } ZlibDecompressor;
 
+#define ZlibDecompressor_CAST(op)   ((ZlibDecompressor *)(op))
+
 /*[clinic input]
 class zlib.ZlibDecompressor "ZlibDecompressor *" "&ZlibDecompressorType"
 [clinic start generated code]*/
 /*[clinic end generated code: output=da39a3ee5e6b4b0d input=0658178ab94645df]*/
 
 static void
-ZlibDecompressor_dealloc(ZlibDecompressor *self)
+ZlibDecompressor_dealloc(PyObject *op)
 {
-    PyObject *type = (PyObject *)Py_TYPE(self);
+    PyTypeObject *type = Py_TYPE(op);
+    PyObject_GC_UnTrack(op);
+    ZlibDecompressor *self = ZlibDecompressor_CAST(op);
     PyThread_free_lock(self->lock);
     if (self->is_initialised) {
         inflateEnd(&self->zst);
@@ -1369,10 +1387,19 @@ ZlibDecompressor_dealloc(ZlibDecompressor *self)
     PyMem_Free(self->input_buffer);
     Py_CLEAR(self->unused_data);
     Py_CLEAR(self->zdict);
-    PyObject_Free(self);
+    type->tp_free(self);
     Py_DECREF(type);
 }
 
+static int
+ZlibDecompressor_traverse(PyObject *op, visitproc visit, void *arg)
+{
+    ZlibDecompressor *self = ZlibDecompressor_CAST(op);
+    Py_VISIT(Py_TYPE(op));
+    Py_VISIT(self->zdict);
+    return 0;
+}
+
 static int
 set_inflate_zdict_ZlibDecompressor(zlibstate *state, ZlibDecompressor *self)
 {
@@ -1724,7 +1751,7 @@ ZlibDecompressor__new__(PyTypeObject *cls,
             args, kwargs, format, keywords, &wbits, &zdict)) {
         return NULL;
     }
-    ZlibDecompressor *self = PyObject_New(ZlibDecompressor, cls);
+    ZlibDecompressor *self = ZlibDecompressor_CAST(cls->tp_alloc(cls, 0));
     if (self == NULL) {
         return NULL;
     }
@@ -1932,6 +1959,7 @@ static PyMethodDef zlib_methods[] =
 
 static PyType_Slot Comptype_slots[] = {
     {Py_tp_dealloc, Comp_dealloc},
+    {Py_tp_traverse, compobject_traverse},
     {Py_tp_methods, comp_methods},
     {0, 0},
 };
@@ -1939,12 +1967,17 @@ static PyType_Slot Comptype_slots[] = {
 static PyType_Spec Comptype_spec = {
     .name = "zlib.Compress",
     .basicsize = sizeof(compobject),
-    .flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_DISALLOW_INSTANTIATION,
+    .flags = (
+        Py_TPFLAGS_DEFAULT
+        | Py_TPFLAGS_DISALLOW_INSTANTIATION
+        | Py_TPFLAGS_HAVE_GC
+    ),
     .slots= Comptype_slots,
 };
 
 static PyType_Slot Decomptype_slots[] = {
     {Py_tp_dealloc, Decomp_dealloc},
+    {Py_tp_traverse, compobject_traverse},
     {Py_tp_methods, Decomp_methods},
     {Py_tp_members, Decomp_members},
     {0, 0},
@@ -1953,12 +1986,17 @@ static PyType_Slot Decomptype_slots[] = {
 static PyType_Spec Decomptype_spec = {
     .name = "zlib.Decompress",
     .basicsize = sizeof(compobject),
-    .flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_DISALLOW_INSTANTIATION,
+    .flags = (
+        Py_TPFLAGS_DEFAULT
+        | Py_TPFLAGS_DISALLOW_INSTANTIATION
+        | Py_TPFLAGS_HAVE_GC
+    ),
     .slots = Decomptype_slots,
 };
 
 static PyType_Slot ZlibDecompressor_type_slots[] = {
     {Py_tp_dealloc, ZlibDecompressor_dealloc},
+    {Py_tp_traverse, ZlibDecompressor_traverse},
     {Py_tp_members, ZlibDecompressor_members},
     {Py_tp_new, ZlibDecompressor__new__},
     {Py_tp_doc, (char *)ZlibDecompressor__new____doc__},
@@ -1973,7 +2011,11 @@ static PyType_Spec ZlibDecompressor_type_spec = {
     // ZlibDecompressor_type_spec does not have Py_TPFLAGS_BASETYPE flag
     // which prevents to create a subclass.
     // So calling PyType_GetModuleState() in this file is always safe.
-    .flags = (Py_TPFLAGS_DEFAULT | Py_TPFLAGS_IMMUTABLETYPE),
+    .flags = (
+        Py_TPFLAGS_DEFAULT
+        | Py_TPFLAGS_IMMUTABLETYPE
+        | Py_TPFLAGS_HAVE_GC
+    ),
     .slots = ZlibDecompressor_type_slots,
 };
 PyDoc_STRVAR(zlib_module_documentation,