diff --git a/lisp/org-clock.el b/lisp/org-clock.el
index ce26a98b4..87bba4bc0 100644
--- a/lisp/org-clock.el
+++ b/lisp/org-clock.el
@@ -1590,18 +1590,19 @@ to, overriding the existing value of `org-clock-out-switch-to-state'."
 		m (floor (/ s 60))
 		s (- s (* 60 s)))
 	  (insert " => " (format "%2d:%02d" h m))
-	  (when (setq remove (and org-clock-out-remove-zero-time-clocks
-				  (= (+ h m) 0)))
-	    (beginning-of-line 1)
-	    (delete-region (point) (point-at-eol))
-	    (and (looking-at "\n") (> (point-max) (1+ (point)))
-		 (delete-char 1)))
 	  (move-marker org-clock-marker nil)
 	  (move-marker org-clock-hd-marker nil)
-	  (when org-log-note-clock-out
-	    (org-add-log-setup
-	     'clock-out nil nil nil
-	     (concat "# Task: " (org-get-heading t) "\n\n")))
+	  ;; Possibly remove zero time clocks.  However, do not add
+	  ;; a note associated to the CLOCK line in this case.
+	  (cond ((and org-clock-out-remove-zero-time-clocks
+		      (= (+ h m) 0))
+		 (setq remove t)
+		 (delete-region (line-beginning-position)
+				(line-beginning-position 2)))
+		(org-log-note-clock-out
+		 (org-add-log-setup
+		  'clock-out nil nil nil
+		  (concat "# Task: " (org-get-heading t) "\n\n"))))
 	  (when org-clock-mode-line-timer
 	    (cancel-timer org-clock-mode-line-timer)
 	    (setq org-clock-mode-line-timer nil))
diff --git a/lisp/org.el b/lisp/org.el
index e93000418..e7d6b571b 100644
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -13815,7 +13815,10 @@ EXTRA is additional text that will be inserted into the notes buffer."
 	 ;; Find location for the new note.
 	 (goto-char org-log-note-marker)
 	 (set-marker org-log-note-marker nil)
-	 (goto-char (org-log-beginning t))
+	 ;; Note associated to a clock is to be located right after
+	 ;; the clock.  Do not move point.
+	 (unless (eq org-log-note-purpose 'clock-out)
+	   (goto-char (org-log-beginning t)))
 	 ;; Make sure point is at the beginning of an empty line.
 	 (cond ((not (bolp)) (let ((inhibit-read-only t)) (insert "\n")))
 	       ((looking-at "[ \t]*\\S-") (save-excursion (insert "\n"))))