diff --git a/gnu/packages/python-xyz.scm b/gnu/packages/python-xyz.scm
index bffb643258..ce4695a956 100644
--- a/gnu/packages/python-xyz.scm
+++ b/gnu/packages/python-xyz.scm
@@ -16003,17 +16003,15 @@ several utilities, as well as an API for building localization tools.")
 (define-public python-packaging
   (package
     (name "python-packaging")
-    (version "20.0")
-    (source
-      (origin
-        (method url-fetch)
-        (uri (pypi-uri "packaging" version))
-        ;; XXX: The URL in the patch file is wrong, it should be
-        ;; <https://github.com/pypa/packaging/pull/256>.
-        (patches (search-patches "python-packaging-test-arch.patch"))
-        (sha256
-         (base32
-          "1y2ip3a4ykkpgnwgn85j6hkspcl0cg3mzms97f40mk57vwqq67gy"))))
+    ;; Note: when updating this, be careful not to change the 'bootstrap'
+    ;; variant below, which can only be updated on 'core-updates'.
+    (version "20.4")
+    (source (origin
+              (method url-fetch)
+              (uri (pypi-uri "packaging" version))
+              (sha256
+               (base32
+                "1y3rc1ams1i25calk6b9jf1gl85ix5a23a146swjvhdr8x7zfms3"))))
     (build-system python-build-system)
     (arguments
      `(#:phases (modify-phases %standard-phases
@@ -16046,25 +16044,26 @@ information.")
 ;; Variants with minimal dependencies, for bootstrapping Pytest.
 (define-public python-packaging-bootstrap
   (hidden-package
-   (package/inherit
-    python-packaging
-    (name "python-packaging-bootstrap")
-    (native-inputs '())
-    (propagated-inputs
-     `(("python-pyparsing" ,python-pyparsing)))
-    (arguments '(#:tests? #f)))))
+   (package
+     (inherit python-packaging)
+     (version "20.0")
+     (source (origin
+               (method url-fetch)
+               (uri (pypi-uri "packaging" version))
+               ;; XXX: The URL in the patch file is wrong, it should be
+               ;; <https://github.com/pypa/packaging/pull/256>.
+               (patches (search-patches "python-packaging-test-arch.patch"))
+               (sha256
+                (base32
+                 "1y2ip3a4ykkpgnwgn85j6hkspcl0cg3mzms97f40mk57vwqq67gy"))))
+     (name "python-packaging-bootstrap")
+     (native-inputs '())
+     (propagated-inputs
+      `(("python-pyparsing" ,python-pyparsing)))
+     (arguments '(#:tests? #f)))))
 
 (define-public python2-packaging-bootstrap
-  (hidden-package
-   (package/inherit
-    python2-packaging
-    (name "python2-packaging-bootstrap")
-    (native-inputs '())
-    (propagated-inputs
-     `(("python-pyparsing" ,python2-pyparsing)))
-    (arguments
-     `(#:tests? #f
-       ,@(package-arguments python2-packaging))))))
+  (package-with-python2 python-packaging-bootstrap))
 
 (define-public python-relatorio
   (package