diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -1142,12 +1142,19 @@
 
 #include "clinic/zlibmodule.c.h"
 
+#define ZLIB_COMPRESS___COPY___METHODDEF    \
+    {"__copy__", (PyCFunction)zlib_Compress_copy, METH_NOARGS, zlib_Compress_copy__doc__},
+
+#define ZLIB_DECOMPRESS___COPY___METHODDEF    \
+    {"__copy__", (PyCFunction)zlib_Decompress_copy, METH_NOARGS, zlib_Decompress_copy__doc__},
+
 static PyMethodDef comp_methods[] =
 {
     ZLIB_COMPRESS_COMPRESS_METHODDEF
     ZLIB_COMPRESS_FLUSH_METHODDEF
 #ifdef HAVE_ZLIB_COPY
     ZLIB_COMPRESS_COPY_METHODDEF
+    ZLIB_COMPRESS___COPY___METHODDEF
 #endif
     {NULL, NULL}
 };
@@ -1158,6 +1165,7 @@
     ZLIB_DECOMPRESS_FLUSH_METHODDEF
 #ifdef HAVE_ZLIB_COPY
     ZLIB_DECOMPRESS_COPY_METHODDEF
+    ZLIB_DECOMPRESS___COPY___METHODDEF
 #endif
     {NULL, NULL}
 };