diff -r 775158408ecb Doc/library/sqlite3.rst
--- a/Doc/library/sqlite3.rst	Sat Aug 27 09:42:40 2016 -0700
+++ b/Doc/library/sqlite3.rst	Sun Aug 28 03:10:33 2016 +0800
@@ -285,11 +285,11 @@
 
       .. versionadded:: 3.2
 
-   .. method:: cursor([cursorClass])
+   .. method:: cursor(factory=sqlite3.Cursor)
 
-      The cursor method accepts a single optional parameter *cursorClass*. If
-      supplied, this must be a custom cursor class that extends
-      :class:`sqlite3.Cursor`.
+      The cursor method accepts a single optional parameter *factory*. If
+      supplied, this must be a callable returning an instance of :class:`sqlite3.Cursor`
+      or its subclasses.
 
    .. method:: commit()
 
diff -r 775158408ecb Lib/sqlite3/test/factory.py
--- a/Lib/sqlite3/test/factory.py	Sat Aug 27 09:42:40 2016 -0700
+++ b/Lib/sqlite3/test/factory.py	Sun Aug 28 03:10:33 2016 +0800
@@ -58,8 +58,17 @@
         self.con.close()
 
     def CheckIsInstance(self):
-        cur = self.con.cursor(factory=MyCursor)
+        cur = self.con.cursor()
+        self.assertIsInstance(cur, sqlite.Cursor)
+        cur = self.con.cursor(MyCursor)
         self.assertIsInstance(cur, MyCursor)
+        cur = self.con.cursor(factory=lambda con: MyCursor(con))
+        self.assertIsInstance(cur, MyCursor)
+
+    def CheckInvalidFactory(self):
+        self.assertRaises(TypeError, self.con.cursor, None)             # not callable
+        self.assertRaises(TypeError, self.con.cursor, lambda: None)     # invalid callable
+        self.assertRaises(TypeError, self.con.cursor, lambda con: None) # return a non-cursor
 
 class RowFactoryTestsBackwardsCompat(unittest.TestCase):
     def setUp(self):
@@ -183,10 +192,12 @@
     def CheckFakeCursorClass(self):
         # Issue #24257: Incorrect use of PyObject_IsInstance() caused
         # segmentation fault.
+        # Issue #27861: Also appies for cursor factory.
         class FakeCursor(str):
             __class__ = sqlite.Cursor
-        cur = self.con.cursor(factory=FakeCursor)
-        self.assertRaises(TypeError, sqlite.Row, cur, ())
+        self.con.row_factory = sqlite.Row
+        self.assertRaises(TypeError, self.con.cursor, FakeCursor)
+        self.assertRaises(TypeError, sqlite.Row, FakeCursor(), ())
 
     def tearDown(self):
         self.con.close()
diff -r 775158408ecb Modules/_sqlite/connection.c
--- a/Modules/_sqlite/connection.c	Sat Aug 27 09:42:40 2016 -0700
+++ b/Modules/_sqlite/connection.c	Sun Aug 28 03:10:33 2016 +0800
@@ -300,7 +300,7 @@
 
 PyObject* pysqlite_connection_cursor(pysqlite_Connection* self, PyObject* args, PyObject* kwargs)
 {
-    static char *kwlist[] = {"factory", NULL, NULL};
+    static char *kwlist[] = {"factory", NULL};
     PyObject* factory = NULL;
     PyObject* cursor;
 
@@ -317,7 +317,16 @@
         factory = (PyObject*)&pysqlite_CursorType;
     }
 
-    cursor = PyObject_CallFunction(factory, "O", self);
+    cursor = PyObject_CallFunctionObjArgs(factory, (PyObject *)self, NULL);
+    if (cursor == NULL)
+        return NULL;
+    if (PyObject_TypeCheck(cursor, &pysqlite_CursorType) == 0) {
+        PyErr_Format(PyExc_TypeError,
+                     "factory must return a cursor, not %s",
+                     Py_TYPE(cursor)->tp_name);
+        Py_DECREF(cursor);
+        return NULL;
+    }
 
     _pysqlite_drop_unused_cursor_references(self);