diff --git a/t/t6036-recursive-corner-cases.sh b/t/t6036-recursive-corner-cases.sh
index 1755073735..9206c22ffb 100755
--- a/t/t6036-recursive-corner-cases.sh
+++ b/t/t6036-recursive-corner-cases.sh
@@ -70,4 +70,80 @@ test_expect_success 'merge simple rename+criss-cross with no modifications' '
 	test $(git rev-parse :1:three) = $(git hash-object merged)
 '
 
+#
+# Same as before, but modify L1 slightly:
+#
+#  L1m L2
+#   o---o
+#  / \ / \
+# o   X   ?
+#  \ / \ /
+#   o---o
+#  R1  R2
+#
+
+test_expect_success 'setup criss-cross + rename merges with basic modification' '
+	git rm -rf . &&
+	git clean -fdqx &&
+	rm -rf .git &&
+	git init &&
+
+	ten="0 1 2 3 4 5 6 7 8 9"
+	for i in $ten
+	do
+		echo line $i in a sample file
+	done >one &&
+	for i in $ten
+	do
+		echo line $i in another sample file
+	done >two &&
+	git add one two &&
+	test_tick && git commit -m initial &&
+
+	git branch L1 &&
+	git checkout -b R1 &&
+	git mv one three &&
+	echo more >>two &&
+	git add two &&
+	test_tick && git commit -m R1 &&
+
+	git checkout L1 &&
+	git mv two three &&
+	test_tick && git commit -m L1 &&
+
+	git checkout L1^0 &&
+	test_tick && git merge -s ours R1 &&
+	git tag L2 &&
+
+	git checkout R1^0 &&
+	test_tick && git merge -s ours L1 &&
+	git tag R2
+'
+
+test_expect_failure 'merge criss-cross + rename merges with basic modification' '
+	git reset --hard &&
+	git checkout L2^0 &&
+
+	test_must_fail git merge -s recursive R2^0 &&
+
+	test 5 = $(git ls-files -s | wc -l) &&
+	test 3 = $(git ls-files -u | wc -l) &&
+	test 0 = $(git ls-files -o | wc -l) &&
+
+	test $(git rev-parse :0:one) = $(git rev-parse L2:one) &&
+	test $(git rev-parse :0:two) = $(git rev-parse R2:two) &&
+	test $(git rev-parse :2:three) = $(git rev-parse L2:three) &&
+	test $(git rev-parse :3:three) = $(git rev-parse R2:three) &&
+
+	head -n 10 two >merged &&
+	cp one merge-me &&
+	>empty &&
+	test_must_fail git merge-file \
+		-L "Temporary merge branch 2" \
+		-L "" \
+		-L "Temporary merge branch 1" \
+		merged empty merge-me &&
+	test $(git rev-parse :1:three) = $(git hash-object merged)
+'
+
 test_done