diff --git a/t/t1401-symbolic-ref.sh b/t/t1401-symbolic-ref.sh
index a2a7e94716..fd3aa89a91 100755
--- a/t/t1401-symbolic-ref.sh
+++ b/t/t1401-symbolic-ref.sh
@@ -38,6 +38,18 @@ test_expect_success 'symbolic-ref refuses bare sha1' '
 
 reset_to_sane
 
+test_expect_success 'symbolic-ref reports a non-symbolic ref' '
+	test_must_fail git symbolic-ref refs/heads/foo >out 2>err &&
+	test_must_be_empty out &&
+	test_grep "is not a symbolic ref" err
+'
+
+test_expect_success 'symbolic-ref -q is silent on a non-symbolic ref' '
+	test_must_fail git symbolic-ref -q refs/heads/foo >out 2>err &&
+	test_must_be_empty out &&
+	test_must_be_empty err
+'
+
 test_expect_success 'HEAD cannot be removed' '
 	test_must_fail git symbolic-ref -d HEAD
 '
diff --git a/t/t1402-check-ref-format.sh b/t/t1402-check-ref-format.sh
index cabc516ae9..9dd64662b2 100755
--- a/t/t1402-check-ref-format.sh
+++ b/t/t1402-check-ref-format.sh
@@ -49,16 +49,19 @@ invalid_ref 'foo/./bar'
 invalid_ref 'foo/bar/.'
 invalid_ref '.refs/foo'
 invalid_ref 'refs/heads/foo.'
-invalid_ref 'heads/foo..bar'
-invalid_ref 'heads/foo?bar'
+for c in '?' '~' '^' ':' '*' '[' ' ' '\' '..'
+do
+	invalid_ref "heads/foo${c}bar"
+done
 valid_ref 'foo./bar'
 invalid_ref 'heads/foo.lock'
 invalid_ref 'heads///foo.lock'
 invalid_ref 'foo.lock/bar'
 invalid_ref 'foo.lock///bar'
 valid_ref 'heads/foo@bar'
+valid_ref 'refs/@'
+invalid_ref '@' --allow-onelevel
 invalid_ref 'heads/v@{ation'
-invalid_ref 'heads/foo\bar'
 invalid_ref "$(printf 'heads/foo\t')"
 invalid_ref "$(printf 'heads/foo\177')"
 valid_ref "$(printf 'heads/fu\303\237')"