diff --git a/lisp/server.el b/lisp/server.el
index 1b027f88ce..e88cffa8fb 100644
--- a/lisp/server.el
+++ b/lisp/server.el
@@ -1780,17 +1780,25 @@ server-save-buffers-kill-terminal
 
 If emacsclient was started with a list of filenames to edit, then
 only these files will be asked to be saved."
-  (if server-stop-automatically
-      (server-stop-automatically--handle-delete-frame (selected-frame))
   (let ((proc (frame-parameter nil 'client)))
     (cond ((eq proc 'nowait)
 	   ;; Nowait frames have no client buffer list.
-	     (if (cdr (frame-list))
+	   (if (length> (frame-list) (if server-stop-automatically 2 1))
+               ;; If there are any other frames, only delete this one.
+               ;; When `server-stop-automatically' is set, don't count
+               ;; the daemon frame.
 	       (progn (save-some-buffers arg)
 		      (delete-frame))
 	     ;; If we're the last frame standing, kill Emacs.
 	     (save-buffers-kill-emacs arg)))
 	  ((processp proc)
+           (if (or (not server-stop-automatically)
+                   (length> server-clients 1)
+                   (seq-some
+                    (lambda (frame)
+                      (when-let ((p (frame-parameter frame 'client)))
+                        (not (eq proc p))))
+                    (frame-list)))
 	       (let ((buffers (process-get proc 'buffers)))
 	         (save-some-buffers
 	          arg (if buffers
@@ -1801,31 +1809,20 @@ server-save-buffers-kill-terminal
                         ;; ARG is non-nil), since we're not killing
                         ;; Emacs (unlike `save-buffers-kill-emacs').
 		        (and arg t)))
-	       (server-delete-client proc)))
-	    (t (error "Invalid client frame"))))))
+	         (server-delete-client proc))
+             ;; If `server-stop-automatically' is set, there are no
+             ;; other client processes, and no other client frames
+             ;; (e.g. `nowait' frames), kill Emacs.
+             (save-buffers-kill-emacs arg)))
+	  (t (error "Invalid client frame")))))
 
 (defun server-stop-automatically--handle-delete-frame (frame)
   "Handle deletion of FRAME when `server-stop-automatically' is used."
-  (when server-stop-automatically
-    (if (if (and (processp (frame-parameter frame 'client))
-		 (eq this-command 'save-buffers-kill-terminal))
-	    (progn
-	      (dolist (f (frame-list))
-		(when (and (eq (frame-parameter frame 'client)
-			       (frame-parameter f 'client))
-			   (not (eq frame f)))
-		  (set-frame-parameter f 'client nil)
-		  (let ((server-stop-automatically nil))
-		    (delete-frame f))))
-	      (if (cddr (frame-list))
-		  (let ((server-stop-automatically nil))
-		    (delete-frame frame)
-		    nil)
-		t))
+  (when (and server-stop-automatically
              (null (cddr (frame-list))))
     (let ((server-stop-automatically nil))
       (save-buffers-kill-emacs)
-	  (delete-frame frame)))))
+      (delete-frame frame))))
 
 (defun server-stop-automatically--maybe-kill-emacs ()
   "Handle closing of Emacs daemon when `server-stop-automatically' is used."