diff --git a/gnu/packages/tls.scm b/gnu/packages/tls.scm
index 90211c733d..9aa0b5a212 100644
--- a/gnu/packages/tls.scm
+++ b/gnu/packages/tls.scm
@@ -418,10 +418,10 @@ required structures.")
                       (doc    #$output:doc)
                       (man-target (string-append doc "/share/man/man3"))
                       (html-target (string-append doc "/share/doc/openssl")))
-                 (copy-recursively man3 man-target)
-                 (delete-file-recursively man3)
-                 (copy-recursively html html-target)
-                 (delete-file-recursively html))))
+                 (mkdir-p (dirname man3-target))
+                 (mkdir-p (dirname html-target))
+                 (rename-file man3 man-target)
+                 (rename-file html html-target))))
         (add-after
          'install 'remove-miscellany
          (lambda _