diff --git a/Doc/c-api/structures.rst b/Doc/c-api/structures.rst
index 87bd362..9f6a5e2 100644
--- a/Doc/c-api/structures.rst
+++ b/Doc/c-api/structures.rst
@@ -273,7 +273,10 @@
 
    :cmacro:`T_OBJECT` and :cmacro:`T_OBJECT_EX` differ in that
    :cmacro:`T_OBJECT` returns ``None`` if the member is *NULL* and
-   :cmacro:`T_OBJECT_EX` raises an :exc:`AttributeError`.
+   :cmacro:`T_OBJECT_EX` raises an :exc:`AttributeError`.  Try to use
+   :cmacro:`T_OBJECT_EX` over :cmacro:`T_OBJECT` because :cmacro:`T_OBJECT_EX`
+   handles use of the :stmt:`del` statement on that attribute more correctly
+   than :cmacro:`T_OBJECT`.
 
    :attr:`flags` can be 0 for write and read access or :cmacro:`READONLY` for
    read-only access.  Using :cmacro:`T_STRING` for :attr:`type` implies
diff --git a/Lib/test/test_descr.py b/Lib/test/test_descr.py
index c31728e..c436eb6 100644
--- a/Lib/test/test_descr.py
+++ b/Lib/test/test_descr.py
@@ -1040,6 +1040,11 @@
             del h
         self.assertEqual(s.getvalue(), '')
 
+        class X(object):
+            __slots__ = "a"
+        with self.assertRaises(AttributeError):
+            del X().a
+
     def test_slots_special(self):
         # Testing __dict__ and __weakref__ in __slots__...
         class D(object):
diff --git a/Misc/NEWS b/Misc/NEWS
index 923cd30..c3f3295 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,9 @@
 Core and Builtins
 -----------------
 
+- Issue #7604: Deleting an unset slotted attribute did not raise an
+  AttributeError.
+
 - Issue #7534: Fix handling of IEEE specials (infinities, nans,
   negative zero) in ** operator.  The behaviour now conforms to that
   described in C99 Annex F.
diff --git a/Python/structmember.c b/Python/structmember.c
index 9f08a6b..8edc354 100644
--- a/Python/structmember.c
+++ b/Python/structmember.c
@@ -104,17 +104,27 @@
 {
 	PyObject *oldv;
 
+	addr += l->offset;
+
 	if ((l->flags & READONLY) || l->type == T_STRING)
 	{
 		PyErr_SetString(PyExc_AttributeError, "readonly attribute");
 		return -1;
 	}
-	if (v == NULL && l->type != T_OBJECT_EX && l->type != T_OBJECT) {
-		PyErr_SetString(PyExc_TypeError,
-				"can't delete numeric/char attribute");
-		return -1;
+	if (v == NULL) {
+		if (l->type == T_OBJECT_EX) {
+			/* Check if the attribute is set. */
+			if (*(PyObject **)addr == NULL) {
+				PyErr_SetString(PyExc_AttributeError, l->name);
+				return -1;
+			}
+		}
+		else if (l->type != T_OBJECT) {
+			PyErr_SetString(PyExc_TypeError,
+					"can't delete numeric/char attribute");
+			return -1;
+		}
 	}
-	addr += l->offset;
 	switch (l->type) {
 	case T_BOOL:{
 		if (!PyBool_Check(v)) {