diff --git a/lisp/progmodes/perl-mode.el b/lisp/progmodes/perl-mode.el
index 7b7a2cdf019..c5d5d703fc9 100644
--- a/lisp/progmodes/perl-mode.el
+++ b/lisp/progmodes/perl-mode.el
@@ -215,11 +215,16 @@
 (eval-and-compile
   (defconst perl--syntax-exp-intro-keywords
     '("split" "if" "unless" "until" "while" "print" "printf"
-      "grep" "map" "not" "or" "and" "for" "foreach" "return"))
+      "grep" "map" "not" "or" "and" "for" "foreach" "return" "die"
+      "warn" "eval"))
 
   (defconst perl--syntax-exp-intro-regexp
     (concat "\\(?:\\(?:^\\|[^$@&%[:word:]]\\)"
             (regexp-opt perl--syntax-exp-intro-keywords)
+            ;; A HERE document as an argument to printf?
+            ;; when printing to a filehandle.
+            "\\|printf?[ \t]*$?[_[:alpha:]][_[:alnum:]]*"
+            "\\|=>"
             "\\|[?:.,;|&*=!~({[]"
             "\\|[^-+][-+]"    ;Bug#42168: `+' is intro but `++' isn't!
             "\\|\\(^\\)\\)[ \t\n]*")))
@@ -335,7 +340,7 @@
         "<<\\(~\\)?[ \t]*\\('[^'\n]*'\\|\"[^\"\n]*\"\\|\\\\[[:alpha:]][[:alnum:]]*\\)"
         ;; The <<EOF case which needs perl--syntax-exp-intro-regexp, to
         ;; disambiguate with the left-bitshift operator.
-        "\\|" perl--syntax-exp-intro-regexp "<<\\(?2:\\sw+\\)\\)"
+        "\\|" perl--syntax-exp-intro-regexp "<<\\(?1:~\\)?\\(?2:\\sw+\\)\\)"
         ".*\\(\n\\)")
        (4 (let* ((eol (match-beginning 4))
                  (st (get-text-property eol 'syntax-table))
diff --git a/test/lisp/progmodes/cperl-mode-resources/here-docs.pl b/test/lisp/progmodes/cperl-mode-resources/here-docs.pl
index bb3d4871a91..13d879bf762 100644
--- a/test/lisp/progmodes/cperl-mode-resources/here-docs.pl
+++ b/test/lisp/progmodes/cperl-mode-resources/here-docs.pl
@@ -140,4 +140,70 @@ =head2 Test case 6
 
 . 'indent-level'; # Continuation, should be indented
 
+=head2 Test case 7
+
+An indented HERE document using a bare identifier.
+
+=cut
+
+## test case
+
+$text = <<~HERE;
+look-here
+HERE
+
+$noindent = "New statement in this line";
+
+=head2 Test case 8
+
+A HERE document as an argument to print when printing to a filehandle.
+
+=cut
+
+## test case
+
+print $fh <<~HERE;
+look-here
+HERE
+
+$noindent = "New statement in this line";
+
+=head2 Test case 9
+
+A HERE document as a hash value.
+
+=cut
+
+my %foo = (
+    text => <<~HERE
+look-here
+HERE
+    );
+
+$noindent = "New statement in this line";
+
+=head2 Test case 10
+
+A HERE document as an argument to die.
+
+=cut
+
+1 or die <<HERE;
+look-here
+HERE
+
+$noindent = "New statement in this line";
+
+=head2 Test case 11
+
+A HERE document as an argument to warn.
+
+=cut
+
+1 or warn <<HERE;
+look-here
+HERE
+
+$noindent = "New statement in this line";
+
 __END__