diff --git a/lisp/emacs-lisp/package-vc.el b/lisp/emacs-lisp/package-vc.el
index a18841fb64d..1dc427d13ac 100644
--- a/lisp/emacs-lisp/package-vc.el
+++ b/lisp/emacs-lisp/package-vc.el
@@ -485,10 +485,21 @@ package-vc--unpack-1
                 lm--prepare-package-dependencies
                 (nconc deps)
                 (setq deps))))))
-      (dolist (dep deps)
-        (cl-callf version-to-list (cadr dep)))
-      (setf (package-desc-reqs pkg-desc) deps)
-      (setf missing (package-vc-install-dependencies (delete-dups deps)))
+      (setf (package-desc-reqs pkg-desc)
+            (cl-loop with lessp = (lambda (a b)
+	                            (if (eq (car a) (car b))
+		                        (version< (cadr b) (cadr b))
+		                      (value< (car a) (car b))))
+                     ;; sort the dependency list to have the newest
+                     ;; versions at the end of the list, so that when
+                     ;; iterating through the list we only request to
+                     ;; install the newest necessary dependency:
+                     with deps = (sort deps :lessp lessp)
+                     for rest on (cdr deps)
+                     for (name vers) in deps
+                     unless (assq name deps)
+                     collect (list name (version-to-list vers))))
+      (setf missing (package-vc-install-dependencies deps))
       (setf missing (delq (assq (package-desc-name pkg-desc)
                                 missing)
                           missing)))