diff --git a/lisp/org-agenda.el b/lisp/org-agenda.el
index 72292fb4e..cc7cb5527 100644
--- a/lisp/org-agenda.el
+++ b/lisp/org-agenda.el
@@ -10526,7 +10526,7 @@ (defun org-agenda-add-entry-to-org-agenda-diary-file (type text &optional d1 d2)
       (anniversary
        (or (re-search-forward "^\\*[ \t]+Anniversaries" nil t)
 	   (progn
-	     (or (org-at-heading-p t)
+	     (or (org-at-heading-p)
 		 (progn
 		   (outline-next-heading)
 		   (insert "* Anniversaries\n\n")
diff --git a/lisp/org-colview.el b/lisp/org-colview.el
index 082d6def0..15cab35f0 100644
--- a/lisp/org-colview.el
+++ b/lisp/org-colview.el
@@ -699,7 +699,7 @@ (defun org-columns--call (fun)
   (let ((hide-body (and (/= (line-end-position) (point-max))
 			(save-excursion
 			  (move-beginning-of-line 2)
-			  (org-at-heading-p t)))))
+			  (org-at-heading-p)))))
     (unwind-protect (funcall fun)
       (when hide-body (outline-hide-entry)))))
 
@@ -1026,7 +1026,7 @@ (defun org-columns-store-format ()
 	      ;; No COLUMNS keyword in the buffer.  Insert one at the
 	      ;; beginning, right before the first heading, if any.
 	      (goto-char (point-min))
-	      (unless (org-at-heading-p t) (outline-next-heading))
+	      (unless (org-at-heading-p) (outline-next-heading))
 	      (let ((inhibit-read-only t))
 		(insert-before-markers "#+COLUMNS: " fmt "\n"))))
 	  (setq-local org-columns-default-format fmt))))))
diff --git a/lisp/org.el b/lisp/org.el
index f59d2cfb0..b17a5477c 100644
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -17243,7 +17243,7 @@ (defun org-toggle-heading (&optional nstars)
 	;; Case 1. Started at an heading: de-star headings.
 	((org-at-heading-p)
 	 (while (< (point) end)
-	   (when (org-at-heading-p t)
+	   (when (org-at-heading-p)
 	     (looking-at org-outline-regexp) (replace-match "")
 	     (setq toggled t))
 	   (forward-line)))
@@ -17844,7 +17844,7 @@ (defun org-context ()
 	 (p (point)) clist o)
     ;; First the large context
     (cond
-     ((org-at-heading-p t)
+     ((org-at-heading-p)
       (push (list :headline (point-at-bol) (point-at-eol)) clist)
       (when (progn
 	      (beginning-of-line 1)
@@ -19594,9 +19594,13 @@ (defun org-before-first-heading-p ()
        (end-of-line)
        (null (re-search-backward org-outline-regexp-bol nil t))))))
 
-(defun org-at-heading-p (&optional _)
-  "Non-nil when on a headline."
-  (outline-on-heading-p t))
+(defun org-at-heading-p (&optional invisible-not-ok)
+  "Return t if point is on a (possibly invisible) heading line.
+If INVISIBLE-NOT-OK is non-nil, an invisible heading line is not ok."
+  (save-excursion
+    (beginning-of-line)
+    (and (bolp) (or (not invisible-not-ok) (not (org-fold-folded-p)))
+	 (looking-at outline-regexp))))
 
 (defun org-in-commented-heading-p (&optional no-inheritance element)
   "Non-nil if point is under a commented heading.