diff --git a/ext/Devel-Peek/t/Peek.t b/ext/Devel-Peek/t/Peek.t
index 53f1c8b2d360..d6f1f21e68a5 100644
--- a/ext/Devel-Peek/t/Peek.t
+++ b/ext/Devel-Peek/t/Peek.t
@@ -534,7 +534,7 @@ do_test('string with Unicode',
                 . '"\\\0 \[UTF8 "\\\x\{100\}\\\x\{0\}\\\x\{200\}"\]
   CUR = 5
   LEN = \\d+
-  COW_REFCNT = 1					# $] < 5.019007
+  COW_REFCNT = 1					# $] < 5.019007 || $] >=5.041000
 ');
 
 do_test('reference to hash containing Unicode',
@@ -558,7 +558,7 @@ do_test('reference to hash containing Unicode',
       PV = $ADDR "' . $cp200_bytes . '"\\\0 \[UTF8 "\\\x\{200\}"\]
       CUR = 2
       LEN = \\d+
-      COW_REFCNT = 1				# $] < 5.019007
+      COW_REFCNT = 1				# $] < 5.019007 || $] >=5.041000
 ',      '',
 	$] >= 5.015
 	    ? undef
diff --git a/op.c b/op.c
index 3fc23eca49af..cd1b07017e5a 100644
--- a/op.c
+++ b/op.c
@@ -5081,7 +5081,9 @@ S_fold_constants(pTHX_ OP *const o)
         SvPADTMP_off(sv);
     else if (!SvIMMORTAL(sv)) {
         SvPADTMP_on(sv);
-        SvREADONLY_on(sv);
+        /* Do not set SvREADONLY(sv) here. newSVOP will call
+         * Perl_ck_svconst, which will do it. Setting it early
+         * here prevents Perl_ck_svconst from setting SvIsCOW(sv).*/
     }
     newop = newSVOP(OP_CONST, 0, MUTABLE_SV(sv));
     if (!is_stringify) newop->op_folded = 1;
diff --git a/t/op/undef.t b/t/op/undef.t
index cce5885b323e..fdba6f6771e1 100644
--- a/t/op/undef.t
+++ b/t/op/undef.t
@@ -165,7 +165,9 @@ SKIP: {
     my $out = runperl(stderr => 1,
                   progs => [ split /\n/, <<'EOS' ]);
     require Devel::Peek;
-    my $f = q(x) x 40; $f = undef;
+    my $f = q(x) x 40;
+    chop $f; # Make sure that the PV buffer is not COWed
+    $f = undef;
     Devel::Peek::Dump($f);
     undef $f;
     Devel::Peek::Dump($f);