diff --git a/numpy/core/src/umath/ufunc_object.c b/numpy/core/src/umath/ufunc_object.c
index aacf3f780c99..077d56c3df26 100644
--- a/numpy/core/src/umath/ufunc_object.c
+++ b/numpy/core/src/umath/ufunc_object.c
@@ -555,8 +555,14 @@ ufunc_get_name_cstr(PyUFuncObject *ufunc) {
  * Parses the positional and keyword arguments for a generic ufunc call.
  *
  * Note that if an error is returned, the caller must free the
- * non-zero references in out_op.  This
- * function does not do its own clean-up.
+ * non-zero references in out_op.  This function does not do its own clean-up.
+ *
+ * Note also that some of the outputs for keyword arguments contain
+ * borrowed references, while others are new references. In particular,
+ * out_extobj: borrowed ref.
+ * out_typetup: new ref.
+ * out_wheremask: new ref.
+ * out_axes: borrowed ref.
  */
 static int
 get_ufunc_arguments(PyUFuncObject *ufunc,
@@ -851,7 +857,7 @@ get_ufunc_arguments(PyUFuncObject *ufunc,
                         if (dtype != NULL) {
                             if (*out_typetup != NULL) {
                                 PyErr_SetString(PyExc_RuntimeError,
-                                    "cannot specify both 'sig' and 'dtype'");
+                                    "cannot specify both 'signature' and 'dtype'");
                                 goto fail;
                             }
                             *out_typetup = Py_BuildValue("(N)", dtype);
@@ -965,7 +971,7 @@ get_ufunc_arguments(PyUFuncObject *ufunc,
                         }
                         if (*out_typetup != NULL) {
                             PyErr_SetString(PyExc_RuntimeError,
-                                    "cannot specify both 'sig' and 'dtype'");
+                                    "cannot specify both 'signature' and 'dtype'");
                             goto fail;
                         }
                         *out_typetup = value;
@@ -1027,18 +1033,19 @@ get_ufunc_arguments(PyUFuncObject *ufunc,
 
 fail:
     Py_XDECREF(str_key_obj);
-    Py_XDECREF(*out_extobj);
-    *out_extobj = NULL;
+    /*
+     * Set output kwargs to NULL, XDECREF'ing those that were not borrowed.
+     */
     Py_XDECREF(*out_typetup);
     *out_typetup = NULL;
-    if (out_axes != NULL) {
-        Py_XDECREF(*out_axes);
-        *out_axes = NULL;
-    }
+    *out_extobj = NULL;
     if (out_wheremask != NULL) {
         Py_XDECREF(*out_wheremask);
         *out_wheremask = NULL;
     }
+    if (out_axes != NULL) {
+        *out_axes = NULL;
+    }
     return -1;
 }
 
@@ -2239,8 +2246,10 @@ PyUFunc_GeneralizedFunction(PyUFuncObject *ufunc,
     NPY_ORDER order = NPY_KEEPORDER;
     /* Use the default assignment casting rule */
     NPY_CASTING casting = NPY_DEFAULT_ASSIGN_CASTING;
-    /* When provided, extobj, typetup, and axes contain borrowed references */
-    PyObject *extobj = NULL, *type_tup = NULL, *axes = NULL;
+    /* When provided, extobj and axes contain borrowed references */
+    PyObject *extobj = NULL, *axes = NULL;
+    /* but type_tup has its own reference */
+    PyObject *type_tup = NULL;
     int keepdims = -1;
 
     if (ufunc == NULL) {
@@ -2772,8 +2781,10 @@ PyUFunc_GenericFunction(PyUFuncObject *ufunc,
     NPY_ORDER order = NPY_KEEPORDER;
     /* Use the default assignment casting rule */
     NPY_CASTING casting = NPY_DEFAULT_ASSIGN_CASTING;
-    /* When provided, extobj and typetup contain borrowed references */
-    PyObject *extobj = NULL, *type_tup = NULL;
+    /* When provided, extobj contains a borrowed reference */
+    PyObject *extobj = NULL;
+    /* but type_tup has its own reference */
+    PyObject *type_tup = NULL;
 
     if (ufunc == NULL) {
         PyErr_SetString(PyExc_ValueError, "function not supported");
diff --git a/numpy/core/tests/test_ufunc.py b/numpy/core/tests/test_ufunc.py
index b7fda3f2e093..ac43464618a2 100644
--- a/numpy/core/tests/test_ufunc.py
+++ b/numpy/core/tests/test_ufunc.py
@@ -36,6 +36,10 @@ def test_sig_dtype(self):
         assert_raises(RuntimeError, np.add, 1, 2, signature='ii->i',
                       dtype=int)
 
+    def test_extobj_refcount(self):
+        # Should not segfault with USE_DEBUG.
+        assert_raises(TypeError, np.add, 1, 2, extobj=[4096], parrot=True)
+
 
 class TestUfunc(object):
     def test_pickle(self):
@@ -717,6 +721,10 @@ def test_axes_argument(self):
         assert_raises(ValueError, mm, z, z, out=z[:, 0])
         assert_raises(ValueError, mm, z[1], z, axes=[0, 1])
         assert_raises(ValueError, mm, z, z, out=z[0], axes=[0, 1])
+        # Regular ufuncs should not accept axes.
+        assert_raises(TypeError, np.add, 1., 1., axes=[0])
+        # should be able to deal with bad unrelated kwargs.
+        assert_raises(TypeError, mm, z, z, axes=[0, 1], parrot=True)
 
     def test_keepdims_argument(self):
         # inner1d signature: '(i),(i)->()'
@@ -784,6 +792,8 @@ def test_keepdims_argument(self):
         mm = umt.matrix_multiply
         assert_raises(TypeError, mm, a, b, keepdims=True)
         assert_raises(TypeError, mm, a, b, keepdims=False)
+        # Regular ufuncs should not accept keepdims.
+        assert_raises(TypeError, np.add, 1., 1., keepdims=False)
 
     def test_innerwt(self):
         a = np.arange(6).reshape((2, 3))