diff --git a/NEWS b/NEWS
index 5806d5365..b37d87907 100644
--- a/NEWS
+++ b/NEWS
@@ -12,6 +12,10 @@ New in spot 2.8.0.dev (not yet released)
     works with weak alternating automata" or "product() does not
     support alternating automata".
 
+  - Work around Emacs bug #34341 when rebuilding documentation on a
+    system with Emacs <26.3, GNU TLS >= 3.6, and without ESS or with
+    an obsolete org-mode installed.
+
 New in spot 2.8 (2019-07-10)
 
   Command-line tools:
diff --git a/doc/org/init.el.in b/doc/org/init.el.in
index 74a3d09a6..db416f1ed 100644
--- a/doc/org/init.el.in
+++ b/doc/org/init.el.in
@@ -11,6 +11,13 @@
 (print (org-version nil t t))
 (print (concat "Org " org-version))
 
+; Some combination of GNU TLS and Emacs fail to retrieve archive
+; contents over https.
+; https://www.reddit.com/r/emacs/comments/cdf48c/failed_to_download_gnu_archive/
+; https://debbugs.gnu.org/cgi/bugreport.cgi?bug=34341
+(if (and (version< emacs-version "26.3") (>= libgnutls-version 30600))
+    (setq gnutls-algorithm-priority "NORMAL:-VERS-TLS1.3"))
+
 ; The Org version that ships with emacs is usually too old.
 (when (version< org-version "9.1")
   (warn "Org-mode is too old; attempting to download a more recent version")