diff --git a/src/main/java/org/apache/datasketches/theta/JaccardSimilarity.java b/src/main/java/org/apache/datasketches/theta/JaccardSimilarity.java
index 2fc9d4fe5..7f967198d 100644
--- a/src/main/java/org/apache/datasketches/theta/JaccardSimilarity.java
+++ b/src/main/java/org/apache/datasketches/theta/JaccardSimilarity.java
@@ -100,6 +100,10 @@ public static double[] jaccard(final ThetaSketch sketchA, final ThetaSketch sket
   /**
    * Returns true if the two given sketches have exactly the same hash values and the same
    * theta values. Thus, they are equivalent.
+   *
+   * <p>Note: For very large pairs of sketches, where the configured nominal entries of the sketches
+   * are 2^26, this method may return false even if the two sketches are equal.
+   *
    * @param sketchA the given sketch A
    * @param sketchB the given sketch B
    * @return true if the two given sketches have exactly the same hash values and the same
@@ -116,8 +120,11 @@ public static boolean exactlyEqual(final ThetaSketch sketchA, final ThetaSketch
     final int countB = sketchB.getRetainedEntries(true);
 
     //Create the ThetaUnion
+    final int minK = 1 << ThetaUtil.MIN_LG_NOM_LONGS;
+    final int maxK = 1 << ThetaUtil.MAX_LG_NOM_LONGS;
+    final int newK = max(min(ceilingPowerOf2(countA + countB), maxK), minK);
     final ThetaUnion union =
-        ThetaSetOperation.builder().setNominalEntries(ceilingPowerOf2(countA + countB)).buildUnion();
+        ThetaSetOperation.builder().setNominalEntries(newK).buildUnion();
     union.union(sketchA);
     union.union(sketchB);
     final ThetaSketch unionAB = union.getResult();
diff --git a/src/test/java/org/apache/datasketches/theta/JaccardSimilarityTest.java b/src/test/java/org/apache/datasketches/theta/JaccardSimilarityTest.java
index 4f84c5382..17cadcc92 100644
--- a/src/test/java/org/apache/datasketches/theta/JaccardSimilarityTest.java
+++ b/src/test/java/org/apache/datasketches/theta/JaccardSimilarityTest.java
@@ -233,6 +233,17 @@ public void checkMinK() {
     println(result[0] + ", " + result[1] + ", " + result[2]);
   }
 
+  @Test
+  public void checkMinKExactlyEqual() {
+    UpdatableThetaSketch skA = UpdatableThetaSketch.builder().build(); //4096
+    UpdatableThetaSketch skB = UpdatableThetaSketch.builder().build(); //4096
+    skA.update(1);
+    skB.update(1);
+    assertTrue(exactlyEqual(skA, skB));
+    skB.update(2);
+    assertFalse(exactlyEqual(skA, skB));
+  }
+
   @Test
   public void printlnTest() {
     println("PRINTING: "+this.getClass().getName());