diff --git a/test/meson.build b/test/meson.build
index 463b358..b3538b8 100644
--- a/test/meson.build
+++ b/test/meson.build
@@ -46,6 +46,7 @@ tests = {
 		'composition-3x-partial',
 		'composition-3x-force',
 		'zpos-2x-reverse',
+		'zpos-3x-zero-fb-id',
 	],
 	'dynamic': [
 		'same',
diff --git a/test/test_alloc.c b/test/test_alloc.c
index 1483774..6035029 100644
--- a/test/test_alloc.c
+++ b/test/test_alloc.c
@@ -538,6 +538,36 @@ static const struct test_case tests[] = {
 			},
 		},
 	},
+	{
+		.name = "zpos-3x-zero-fb-id",
+		.needs_composition = false,
+		/* Layers at zpos=1 and zpos=2 can be put on a plane. There is
+		 * a layer with zpos=3 but it's not visible because it has a
+		 * zero FB_ID, so it should be ignored. */
+		.layers = {
+			{
+				.width = 1920,
+				.height = 1080,
+				.props = {{ "zpos", 1 }},
+				.compat = { PRIMARY_PLANE },
+				.result = PRIMARY_PLANE,
+			},
+			{
+				.width = 200,
+				.height = 200,
+				.props = {{ "zpos", 2 }},
+				.compat = { OVERLAY_PLANE },
+				.result = OVERLAY_PLANE,
+			},
+			{
+				.width = 100,
+				.height = 100,
+				.props = {{ "zpos", 3 }, { "FB_ID", 0 }},
+				.compat = { 0 },
+				.result = NULL,
+			},
+		},
+	},
 	{
 		.name = "composition-3x",
 		.needs_composition = true,