diff --git a/lisp/org.el b/lisp/org.el
index 7c1b291f3..ee7965a20 100644
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -7959,7 +7959,7 @@ in the region."
 	 (diff (abs (- level (length down-head) -1))))
     (replace-match down-head nil t)
     ;; Fixup tag positioning
-    (and org-auto-align-tags (org-set-tags nil t))
+    (and org-auto-align-tags (org-set-tags nil 'ignore-column))
     (if org-adapt-indentation (org-fixup-indentation diff))
     (run-hooks 'org-after-demote-entry-hook)))
 
@@ -14457,15 +14457,18 @@ If DATA is nil or the empty string, any tags will be removed."
 (defvar org-indent-indentation-per-level)
 (defun org-set-tags (&optional arg just-align)
   "Set the tags for the current headline.
-With prefix ARG, realign all tags in headings in the current buffer."
+With prefix ARG, realign all tags in headings in the current buffer.
+When JUST-ALIGN is non-nil, only align tags.
+When JUST-ALIGN is 'ignore-column, align tags without trying to set
+the column by ignoring invisible text."
   (interactive "P")
   (if (and (org-region-active-p) org-loop-over-headlines-in-active-region)
       (let ((cl (if (eq org-loop-over-headlines-in-active-region 'start-level)
 		    'region-start-level 'region))
 	    org-loop-over-headlines-in-active-region)
 	(org-map-entries
-	 ;; We don't use ARG and JUST-ALIGN here these args are not
-	 ;; useful when looping over headlines
+	 ;; We don't use ARG and JUST-ALIGN here because these args
+	 ;; are not useful when looping over headlines.
 	 `(org-set-tags)
 	 org-loop-over-headlines-in-active-region
 	 cl (if (outline-invisible-p) (org-end-of-subtree nil t))))
@@ -14554,7 +14557,7 @@ With prefix ARG, realign all tags in headings in the current buffer."
 	  (and (not (featurep 'xemacs)) c0 indent-tabs-mode (tabify p0 (point)))
 	  tags)
 	 (t (error "Tags alignment failed")))
-	(org-move-to-column col nil nil t)
+	(org-move-to-column col nil nil (not (eq just-align 'ignore-column)))
 	(unless just-align
 	  (run-hooks 'org-after-tags-change-hook))))))