diff --git a/tests/test-grammar-integration.cpp b/tests/test-grammar-integration.cpp
index da5c5f98d..0fe6abef1 100644
--- a/tests/test-grammar-integration.cpp
+++ b/tests/test-grammar-integration.cpp
@@ -148,6 +148,33 @@ static void test_simple_grammar() {
             "-10000",
             "-100000000000000000000000000000000",
             "100000000000000000000000000000000",
+            "00",
+            "01",
+            "-0",
+        }
+    );
+    test_schema(
+        "simple min 456",
+        R"""({
+            "type": "integer",
+            "minimum": 456
+        })""",
+        // Passing strings
+        {
+            "456",
+            "4560",
+            "457",
+            "460",
+            "500",
+        },
+        // Failing strings
+        {
+            "455",
+            "356",
+            "50",
+            "050",
+            "-1",
+            "-456",
         }
     );
     test_schema(