diff --git a/doc/texdoc.tex b/doc/texdoc.tex
index ce01c8e..f4b39b6 100644
--- a/doc/texdoc.tex
+++ b/doc/texdoc.tex
@@ -787,13 +787,7 @@ \subsection{Zsh}
 \item adding \code{eval "\$(texdoc \lopt{print-completion} zsh)"} to your
   zsh configuration file.
 
-\item adding a file somewhere in \code{\$fpath} with the following contents:
-%
-\begin{htcode}
-#compdef texdoc
-(( $+functions[__texdoc] )) || eval "$(texdoc \textbackslash
-  --print-completion zsh)" && __texdoc
-\end{htcode}
+\item creating a file named \code{\_texdoc} in \code{\$fpath} whose content is the output of \code{texdoc \lopt{print-completion} zsh}.
 \end{itemize}
 
 \section{Licence}
diff --git a/script/texdoclib-const.tlu b/script/texdoclib-const.tlu
index c551bf4..1340a82 100644
--- a/script/texdoclib-const.tlu
+++ b/script/texdoclib-const.tlu
@@ -50,8 +50,8 @@ Website: <https://tug.org/texdoc/>
 Repository: <https://github.com/TeX-Live/texdoc>
 Please email bugs to <texdoc@tug.org>.]]
 
-zsh_completion = [[
-compdef __texdoc texdoc
+zsh_completion = [=[
+#compdef texdoc
 
 __texdoc() {
   local options=(
@@ -72,7 +72,15 @@ __texdoc() {
     ;;
   esac
 }
-]]
+
+if [[ $zsh_eval_context[-1] == loadautofunc ]]; then
+  # autoload from fpath, call function directly
+  __texdoc "$@"
+else
+  # eval/source/. command, register function for later
+  compdef __texdoc texdoc
+fi
+]=]
 
 --[[ structure of the options table