diff --git a/README.md b/README.md
index 2dc3eec..5efd89c 100644
--- a/README.md
+++ b/README.md
@@ -59,12 +59,11 @@ subcommands and, for `show` and `complete`, the reference argument — by callin
 (`Stdlib` open, package-qualified `/pkg/...` paths, kind tags like `type-`,
 section labels, …). Type `.` or `/` and press TAB again to drill in.
 
-`opam install` puts it under `$OPAM_SWITCH_PREFIX/share/odoc-switchdocs/zsh`.
-That directory isn't on zsh's `$fpath` by default, so add it (before
-`compinit`) in `~/.zshrc`:
+`opam install` puts it under the package's share dir. That directory isn't on
+zsh's `$fpath` by default, so add it (before `compinit`) in `~/.zshrc`:
 
 ```zsh
-fpath=("$OPAM_SWITCH_PREFIX/share/odoc-switchdocs/zsh" $fpath)
+fpath=("$(opam var odoc-switchdocs:share)/zsh" $fpath)
 autoload -U compinit && compinit
 ```
 
diff --git a/completions/zsh/_switchdocs b/completions/zsh/_switchdocs
index cdb096e..131a37f 100644
--- a/completions/zsh/_switchdocs
+++ b/completions/zsh/_switchdocs
@@ -3,9 +3,9 @@
 # zsh completion for switchdocs.
 #
 # Install: put this file's directory on $fpath before compinit. After
-# `opam install` it lives under the switch's share dir; add to ~/.zshrc:
+# `opam install` it lives under the package's share dir; add to ~/.zshrc:
 #
-#     fpath=("$OPAM_SWITCH_PREFIX/share/odoc-switchdocs/zsh" $fpath)
+#     fpath=("$(opam var odoc-switchdocs:share)/zsh" $fpath)
 #     autoload -U compinit && compinit
 #
 # (or point $fpath at completions/zsh in a source checkout.)