diff --git a/pad.c b/pad.c
index d4a20ef84cbb..921c10d1cefa 100644
--- a/pad.c
+++ b/pad.c
@@ -2235,7 +2235,7 @@ S_cv_clone(pTHX_ CV *proto, CV *cv, CV *outside, HV *cloned)
     if (UNLIKELY(CvISXSUB(proto))) {
         CvXSUB(cv)    = CvXSUB(proto);
         CvXSUBANY(cv) = CvXSUBANY(proto);
-        if (CvREFCOUNTED_ANYSV(cv))
+        if (CvREFCOUNTED_ANYSV(cv) || CvCONST(cv))
             SvREFCNT_inc(CvXSUBANY(cv).any_sv);
     }
     else {
diff --git a/t/op/state.t b/t/op/state.t
index 747e316f226a..f309b4ec3fca 100644
--- a/t/op/state.t
+++ b/t/op/state.t
@@ -9,7 +9,7 @@ BEGIN {
 
 use strict;
 
-plan tests => 164;
+plan tests => 166;
 
 # Before loading feature.pm, test it with CORE::
 ok eval 'CORE::state $x = 1;', 'CORE::state outside of feature.pm scope';
@@ -503,6 +503,21 @@ for (1,2) {
     is($s, "-1-", "state with multiconcat pass $_");
 }
 
+# This caused 'Attempt to free unreferenced scalar' because the SV holding
+# the value of the const state sub wasn't having its ref count incremented
+# when the sub was cloned.
+
+{
+    my @warnings;
+    local $SIG{__WARN__} = sub { push @warnings, @_ };
+    my $e = eval 'my $s = sub { state sub FOO () { 42 } }; 1;';
+    is($e, 1, "const state sub ran ok");
+    ok(!@warnings, "no 'Attempt to free unreferenced scalar'")
+        or diag "got these warnings:\n@warnings";
+}
+
+
+
 __DATA__
 (state $a) = 1;
 (state @a) = 1;