diff --git a/lisp/progmodes/python.el b/lisp/progmodes/python.el
index 14b65669c4b..ec5d8c55512 100644
--- a/lisp/progmodes/python.el
+++ b/lisp/progmodes/python.el
@@ -4084,6 +4084,12 @@ JUSTIFY should be used (if applicable) as in `fill-paragraph'."
       (goto-char (line-end-position))))
   t)
 
+(defun python-do-auto-fill ()
+  "Like `do-auto-fill', but bind `fill-indent-according-to-mode'."
+  ;; See Bug#36056.
+  (let ((fill-indent-according-to-mode t))
+    (do-auto-fill)))
+
 
 ;;; Skeletons
 
@@ -5379,7 +5385,7 @@ REPORT-FN is Flymake's callback function."
   (set (make-local-variable 'paragraph-start) "\\s-*$")
   (set (make-local-variable 'fill-paragraph-function)
        #'python-fill-paragraph)
-  (set (make-local-variable 'fill-indent-according-to-mode) t) ; Bug#36056.
+  (set (make-local-variable 'normal-auto-fill-function) #'python-do-auto-fill)
 
   (set (make-local-variable 'beginning-of-defun-function)
        #'python-nav-beginning-of-defun)
diff --git a/test/lisp/progmodes/python-tests.el b/test/lisp/progmodes/python-tests.el
index b1cf7e8806a..c5ad1dfb862 100644
--- a/test/lisp/progmodes/python-tests.el
+++ b/test/lisp/progmodes/python-tests.el
@@ -1351,7 +1351,7 @@ this is an arbitrarily
                       expected)))))
 
 
-;;; Autofill
+;;; Filling
 
 (ert-deftest python-auto-fill-docstring ()
   (python-tests-with-temp-buffer
@@ -1368,6 +1368,17 @@ def some_function(arg1,
      (forward-line 1)
      (should (= docindent (current-indentation))))))
 
+(ert-deftest python-fill-docstring ()
+  (python-tests-with-temp-buffer
+   "\
+r'''aaa
+
+this is a test this is a test this is a test this is a test this is a test this is a test.
+'''"
+   (search-forward "test.")
+   (fill-paragraph)
+   (should (= (current-indentation) 0))))
+
 
 ;;; Mark