diff --git a/lucene/core/src/test/org/apache/lucene/index/Test2BPoints.java b/lucene/core/src/test/org/apache/lucene/index/Test2BPoints.java
index 43207b8ceec..75f2bbe3f47 100644
--- a/lucene/core/src/test/org/apache/lucene/index/Test2BPoints.java
+++ b/lucene/core/src/test/org/apache/lucene/index/Test2BPoints.java
@@ -70,11 +70,12 @@ public class Test2BPoints extends LuceneTestCase {
     }
 
     final int numDocs = (Integer.MAX_VALUE / 26) + 1;
-    long counter = 0;
+    int counter = 0;
     for (int i = 0; i < numDocs; i++) {
       Document doc = new Document();
       for (int j=0;j<26;j++) {
-        doc.add(new LongPoint("long", counter));
+        long x = (((long) random().nextInt() << 32)) | (long) counter;
+        doc.add(new LongPoint("long", x));
         counter++;
       }
       w.addDocument(doc);
@@ -120,7 +121,9 @@ public class Test2BPoints extends LuceneTestCase {
     for (int i = 0; i < numDocs; i++) {
       Document doc = new Document();
       for (int j=0;j<26;j++) {
-        doc.add(new LongPoint("long", counter, 2*counter+1));
+        long x = (((long) random().nextInt() << 32)) | (long) counter;
+        long y = (((long) random().nextInt() << 32)) | (long) random().nextInt();
+        doc.add(new LongPoint("long", x, y));
         counter++;
       }
       w.addDocument(doc);
diff --git a/lucene/core/src/test/org/apache/lucene/util/bkd/Test2BBKDPoints.java b/lucene/core/src/test/org/apache/lucene/util/bkd/Test2BBKDPoints.java
new file mode 100644
index 00000000000..cf184094abc
--- /dev/null
+++ b/lucene/core/src/test/org/apache/lucene/util/bkd/Test2BBKDPoints.java
@@ -0,0 +1,121 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.lucene.util.bkd;
+
+import java.io.IOException;
+
+import org.apache.lucene.analysis.MockAnalyzer;
+import org.apache.lucene.codecs.Codec;
+import org.apache.lucene.codecs.FilterCodec;
+import org.apache.lucene.codecs.PointsFormat;
+import org.apache.lucene.codecs.PointsReader;
+import org.apache.lucene.codecs.PointsWriter;
+import org.apache.lucene.codecs.lucene60.Lucene60PointsReader;
+import org.apache.lucene.codecs.lucene60.Lucene60PointsWriter;
+import org.apache.lucene.document.Document;
+import org.apache.lucene.document.LongPoint;
+import org.apache.lucene.search.IndexSearcher;
+import org.apache.lucene.store.Directory;
+import org.apache.lucene.store.FSDirectory;
+import org.apache.lucene.store.IOContext;
+import org.apache.lucene.store.IndexInput;
+import org.apache.lucene.store.IndexOutput;
+import org.apache.lucene.util.LuceneTestCase.Monster;
+import org.apache.lucene.util.LuceneTestCase.SuppressCodecs;
+import org.apache.lucene.util.LuceneTestCase;
+import org.apache.lucene.util.NumericUtils;
+import org.apache.lucene.util.TestUtil;
+import org.apache.lucene.util.TimeUnits;
+
+import com.carrotsearch.randomizedtesting.annotations.TimeoutSuite;
+
+// e.g. run like this: ant test -Dtestcase=Test2BBKDPoints -Dtests.nightly=true -Dtests.verbose=true -Dtests.monster=true
+// 
+//   or: python -u /l/util/src/python/repeatLuceneTest.py -heap 4g -once -nolog -tmpDir /b/tmp -logDir /l/logs Test2BBKDPoints.test2D -verbose
+
+@TimeoutSuite(millis = 365 * 24 * TimeUnits.HOUR) // hopefully ~1 year is long enough ;)
+@Monster("takes at least 4 hours and consumes many GB of temp disk space")
+public class Test2BBKDPoints extends LuceneTestCase {
+  public void test1D() throws Exception {
+    Directory dir = FSDirectory.open(createTempDir("2BBKDPoints1D"));
+
+    final int numDocs = (Integer.MAX_VALUE / 26) + 100;
+
+    BKDWriter w = new BKDWriter(numDocs, dir, "_0", 1, 1024, 128, Long.BYTES, 26L * numDocs);
+    int counter = 0;
+    byte[] packedBytes = new byte[Long.BYTES];
+    for (int docID = 0; docID < numDocs; docID++) {
+      for (int j=0;j<26;j++) {
+        // first a random int:
+        NumericUtils.intToSortableBytes(random().nextInt(), packedBytes, 0);
+        // then our counter, which will overflow a bit in the end:
+        NumericUtils.intToSortableBytes(counter, packedBytes, Integer.BYTES);
+        w.add(packedBytes, docID);
+        counter++;
+      }
+      if (VERBOSE && docID % 100000 == 0) {
+        System.out.println(docID + " of " + numDocs + "...");
+      }
+    }
+    IndexOutput out = dir.createOutput("1d.bkd", IOContext.DEFAULT);
+    long indexFP = w.finish(out);
+    out.close();
+
+    IndexInput in = dir.openInput("1d.bkd", IOContext.DEFAULT);
+    in.seek(indexFP);
+    BKDReader r = new BKDReader(in);
+    r.verify(numDocs);
+    in.close();
+    dir.close();
+  }
+
+  public void test2D() throws Exception {
+    Directory dir = FSDirectory.open(createTempDir("2BBKDPoints2D"));
+
+    final int numDocs = (Integer.MAX_VALUE / 26) + 100;
+
+    BKDWriter w = new BKDWriter(numDocs, dir, "_0", 2, Long.BYTES, 26L * numDocs);
+    long counter = 0;
+    byte[] packedBytes = new byte[2*Long.BYTES];
+    for (int docID = 0; docID < numDocs; docID++) {
+      for (int j=0;j<26;j++) {
+        // first a random int:
+        NumericUtils.intToSortableBytes(random().nextInt(), packedBytes, 0);
+        // then our counter, which will overflow a bit in the end:
+        NumericUtils.intToSortableBytes(counter, packedBytes, Integer.BYTES);
+        // then two random ints for the 2nd dimension:
+        NumericUtils.intoSortableBytes(random().nextInt(), packedBytes, Long.BYTES);
+        NumericUtils.intoSortableBytes(random().nextInt(), packedBytes, Long.BYTES + Integer.BYTES);
+        w.add(packedBytes, docID);
+        counter++;
+      }
+      if (VERBOSE && docID % 100000 == 0) {
+        System.out.println(docID + " of " + numDocs + "...");
+      }
+    }
+    IndexOutput out = dir.createOutput("2d.bkd", IOContext.DEFAULT);
+    long indexFP = w.finish(out);
+    out.close();
+
+    IndexInput in = dir.openInput("2d.bkd", IOContext.DEFAULT);
+    in.seek(indexFP);
+    BKDReader r = new BKDReader(in);
+    r.verify(numDocs);
+    in.close();
+    dir.close();
+  }
+}