diff --git a/lisp/progmodes/cperl-mode.el b/lisp/progmodes/cperl-mode.el
index 6fe0c018b1d..5ecd5668b34 100644
--- a/lisp/progmodes/cperl-mode.el
+++ b/lisp/progmodes/cperl-mode.el
@@ -3560,19 +3560,18 @@ the sections using `cperl-pod-head-face', `cperl-pod-face',
 	   "\\(\\`\n?\\|^\n\\)="	; POD
 	   "\\|"
 	   ;; One extra () before this:
-	   "<<~?"			; HERE-DOC
-	   "\\("			; 1 + 1
+	   "<<\\(~?\\)"		 ; HERE-DOC, indented-p = capture 2
+	   "\\("			; 2 + 1
 	   ;; First variant "BLAH" or just ``.
 	   "[ \t]*"			; Yes, whitespace is allowed!
-	   "\\([\"'`]\\)"		; 2 + 1 = 3
-	   "\\([^\"'`\n]*\\)"		; 3 + 1
-	   "\\3"
+	   "\\([\"'`]\\)"		; 3 + 1 = 4
+	   "\\([^\"'`\n]*\\)"		; 4 + 1
+	   "\\4"
 	   "\\|"
 	   ;; Second variant: Identifier or \ID (same as 'ID') or empty
-	   "\\\\?\\(\\([a-zA-Z_][a-zA-Z_0-9]*\\)?\\)" ; 4 + 1, 5 + 1
+	   "\\\\?\\(\\([a-zA-Z_][a-zA-Z_0-9]*\\)?\\)" ; 5 + 1, 6 + 1
 	   ;; Do not have <<= or << 30 or <<30 or << $blah.
 	   ;; "\\([^= \t0-9$@%&]\\|[ \t]+[^ \t\n0-9$@%&]\\)" ; 6 + 1
-	   "\\(\\)"		; To preserve count of pars :-( 6 + 1
 	   "\\)"
 	   "\\|"
 	   ;; 1+6 extra () before this:
@@ -3762,11 +3761,11 @@ the sections using `cperl-pod-head-face', `cperl-pod-face',
 	       ;;    ;; "\\([^= \t0-9$@%&]\\|[ \t]+[^ \t\n0-9$@%&]\\)" ; 6 + 1
 	       ;;    "\\(\\)"		; To preserve count of pars :-( 6 + 1
 	       ;;  "\\)"
-	       ((match-beginning 2)	; 1 + 1
+	       ((match-beginning 3)	; 2 + 1
 		(setq b (point)
 		      tb (match-beginning 0)
 		      c (and		; not HERE-DOC
-			 (match-beginning 5)
+			 (match-beginning 6)
 			 (save-match-data
 			   (or (looking-at "[ \t]*(") ; << function_call()
 			       (save-excursion ; 1 << func_name, or $foo << 10
@@ -3793,17 +3792,17 @@ the sections using `cperl-pod-head-face', `cperl-pod-face',
 						   (looking-at "\\(printf?\\|say\\|system\\|exec\\|sort\\)\\>")))
 						(error t)))))))
 				   (error nil))) ; func(<<EOF)
-			       (and (not (match-beginning 6)) ; Empty
+			       (and (not (match-beginning 7)) ; Empty
 				    (looking-at
 				     "[ \t]*[=0-9$@%&(]"))))))
 		(if c			; Not here-doc
 		    nil			; Skip it.
-		  (setq c (match-end 2)) ; 1 + 1
-		  (if (match-beginning 5) ;4 + 1
-		      (setq b1 (match-beginning 5) ; 4 + 1
-			    e1 (match-end 5)) ; 4 + 1
-		    (setq b1 (match-beginning 4) ; 3 + 1
-			  e1 (match-end 4))) ; 3 + 1
+		  (setq c (match-end 3)) ; 2 + 1
+		  (if (match-beginning 6) ;6 + 1
+		      (setq b1 (match-beginning 6) ; 5 + 1
+			    e1 (match-end 6)) ; 5 + 1
+		    (setq b1 (match-beginning 5) ; 4 + 1
+			  e1 (match-end 5))) ; 4 + 1
 		  (setq tag (buffer-substring b1 e1)
 			qtag (regexp-quote tag))
 		  (cond (cperl-pod-here-fontify
@@ -3818,8 +3817,10 @@ the sections using `cperl-pod-head-face', `cperl-pod-face',
 		  (setq b (point))
 		  ;; We do not search to max, since we may be called from
 		  ;; some hook of fontification, and max is random
-		  (or (and (re-search-forward (concat "^[ \t]*" qtag "$")
-					      stop-point 'toend)
+		  (or (and (re-search-forward
+			    (concat "^" (when (equal (match-string 2) "~") "[ \t]*")
+				    qtag "$")
+			    stop-point 'toend)
 			   ;;;(eq (following-char) ?\n) ; XXXX WHY???
 			   )
 		    (progn		; Pretend we matched at the end