--- org.el	2019/12/07 15:36:31	1.1
+++ org.el	2019/12/07 15:37:15
@@ -10824,9 +10824,14 @@
 			(repeater-type (match-string 1 ts)))
 		    (cond
 		     ((equal "." repeater-type)
-		      ;; Shift starting date to today.
-		      (org-timestamp-change (- (org-today) (time-to-days time))
-					    'day))
+		      (cond
+		       ((equal what "h")
+			;; adjust timestamp to now
+			(org-timestamp-change 0 'now))
+		       (t
+			;; Shift starting date to today.
+			(org-timestamp-change (- (org-today) (time-to-days time))
+					      'day))))
 		     ((equal "+" repeater-type)
 		      (let ((nshiftmax 10)
 			    (nshift 0))
@@ -15349,6 +15354,8 @@
 	  (setcar (nthcdr 1 time0) (or (nth 1 time0) 0))
 	  (setcar (nthcdr 2 time0) (or (nth 2 time0) 0))
 	  (setq time (apply 'encode-time time0))))
+      (when (eq what 'now)
+	(setq time (current-time)))
       ;; Insert the new time-stamp, and ensure point stays in the same
       ;; category as before (i.e. not after the last position in that
       ;; category).