diff --git a/Include/unicodeobject.h b/Include/unicodeobject.h
index 0accc1d5c2d..59dcf736b1b 100644
--- a/Include/unicodeobject.h
+++ b/Include/unicodeobject.h
@@ -2263,6 +2263,10 @@ PyAPI_FUNC(Py_UNICODE*) PyUnicode_AsUnicodeCopy(
 PyAPI_FUNC(int) _PyUnicode_CheckConsistency(
     PyObject *op,
     int check_content);
+#elif !defined(NDEBUG)
+/* For asserts that call _PyUnicode_CheckConsistency(), which would
+ * otherwise be a problem when building with asserts but without Py_DEBUG. */
+#define _PyUnicode_CheckConsistency(op, check_content) PyUnicode_Check(op)
 #endif
 
 /* Return an interned Unicode object for an Identifier; may fail if there is no memory.*/
diff --git a/Objects/obmalloc.c b/Objects/obmalloc.c
index 7cc889f817b..9dd8421a339 100644
--- a/Objects/obmalloc.c
+++ b/Objects/obmalloc.c
@@ -1176,7 +1176,7 @@ _PyObject_Alloc(int use_calloc, void *ctx, size_t nelem, size_t elsize)
 
     _Py_AllocatedBlocks++;
 
-    assert(nelem <= PY_SSIZE_T_MAX / elsize);
+    assert(elsize == 0 || nelem <= PY_SSIZE_T_MAX / elsize);
     nbytes = nelem * elsize;
 
 #ifdef WITH_VALGRIND
@@ -2233,7 +2233,9 @@ _PyObject_DebugMallocStats(FILE *out)
 
             if (p->ref.count == 0) {
                 /* currently unused */
+#ifdef Py_DEBUG
                 assert(pool_is_in_list(p, arenas[i].freepools));
+#endif
                 continue;
             }
             ++numpools[sz];