diff --git a/src/test/java/com/fasterxml/jackson/failing/JsonPointer1328Test.java b/src/test/java/com/fasterxml/jackson/failing/JsonPointer1328Test.java
new file mode 100644
index 0000000000..2854fdd3ef
--- /dev/null
+++ b/src/test/java/com/fasterxml/jackson/failing/JsonPointer1328Test.java
@@ -0,0 +1,31 @@
+package com.fasterxml.jackson.failing;
+
+import com.fasterxml.jackson.core.JUnit5TestBase;
+import com.fasterxml.jackson.core.JsonPointer;
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+class JsonPointer1328Test extends JUnit5TestBase
+{
+    // 5k enough on some systems to reproduce; use 10k
+    private final static int DEPTH = 10_000;
+
+    // [core#1328]: verify efficient operation of JsonPointer.head()
+    @Test
+    void deepHead()
+    {
+        final String INPUT = repeat("/a", DEPTH);
+        JsonPointer ptr = JsonPointer.compile(INPUT);
+        assertEquals(repeat("/a", DEPTH - 1), ptr.head().toString());
+    }
+
+    private final static String repeat(String part, int count) {
+        StringBuilder sb = new StringBuilder(count * part.length());
+        while (--count >= 0) {
+            sb.append(part);
+        }
+        return sb.toString();
+    }
+    
+}