diff --git a/lisp/org.el b/lisp/org.el
index ce68f4692..69e333c84 100644
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -11305,8 +11305,9 @@ or a character."
       (user-error "Priority commands are disabled"))
     (setq action (or action 'set))
     (let ((nump (< org-priority-lowest 65))
+          (saved-position (point))
 	  current new news have remove)
-      (save-excursion
+
 	(org-back-to-heading t)
 	(when (looking-at org-priority-regexp)
 	  (let ((ms (match-string 2)))
@@ -11337,7 +11338,7 @@ or a character."
 		     (= (upcase org-priority-lowest) org-priority-lowest))
 	    (setq new (upcase new)))
 	  (cond ((equal new ?\s) (setq remove t))
-		((or (< (upcase new) org-priority-highest) (> (upcase new) org-priority-lowest))
+		((or (> (upcase new) org-priority-highest) (< (upcase new) org-priority-lowest))
 		 (user-error
 		  (if nump
 		      "Priority must be between `%s' and `%s'"
@@ -11364,8 +11365,8 @@ or a character."
 			    org-priority-default
 			  (1+ org-priority-default))))))
 	 (t (user-error "Invalid action")))
-	(when (or (< (upcase new) org-priority-highest)
-		  (> (upcase new) org-priority-lowest))
+	(when (or (> (upcase new) org-priority-highest)
+		  (< (upcase new) org-priority-lowest))
 	  (if (and (memq action '(up down))
 		   (not have) (not (eq last-command this-command)))
 	      ;; `new' is from default priority
@@ -11377,12 +11378,26 @@ or a character."
 	;; Numerical priorities are limited to 64, beyond that number,
 	;; assume the priority cookie is a character.
 	(setq news (if (> new 64) (format "%c" new) (format "%s" new)))
+        ;; Actually setting the priority isn’t so straightforward
+        ;; There are several cases
 	(if have
+            ;; ① have and remove
 	    (if remove
 		(replace-match "" t t nil 1)
-	      (replace-match news t t nil 2))
+              ;; ② have and not remove, i.e., update
+	      (let ((case-fold-search nil)) (looking-at org-priority-regexp))
+              (if (match-end 2)
+		  (progn
+		    (goto-char (match-end 2))
+                    (delete-region (match-beginning 2) (match-end 2))
+		    (insert news))
+	        (goto-char (match-end 1))
+	        (insert "[#" news "] "))
+              )
+          ;; ③ don’t have and remove — nonsense
 	  (if remove
 	      (user-error "No priority cookie found in line")
+            ;; ④ don’t have and not remove, i.e., insert
 	    (let ((case-fold-search nil)) (looking-at org-todo-line-regexp))
 	    (if (match-end 2)
 		(progn
@@ -11390,7 +11405,8 @@ or a character."
 		  (insert " [#" news "]"))
 	      (goto-char (match-beginning 3))
 	      (insert "[#" news "] "))))
-	(org-align-tags))
+	(org-align-tags)
+      (goto-char saved-position)
       (if remove
 	  (message "Priority removed")
 	(message "Priority of current item set to %s" news)))))