diff --git a/lucene/core/src/java/org/apache/lucene/util/automaton/Automata.java b/lucene/core/src/java/org/apache/lucene/util/automaton/Automata.java
index 3bcd31945c7..294700b8499 100644
--- a/lucene/core/src/java/org/apache/lucene/util/automaton/Automata.java
+++ b/lucene/core/src/java/org/apache/lucene/util/automaton/Automata.java
@@ -32,6 +32,7 @@ package org.apache.lucene.util.automaton;
 import java.util.*;
 
 import org.apache.lucene.util.BytesRef;
+import org.apache.lucene.util.StringHelper;
 
 /**
  * Construction of basic automata.
@@ -216,6 +217,16 @@ final public class Automata {
     return s;
   }
 
+  private static boolean suffixIsZeros(BytesRef br, int len) {
+    for(int i=len;i<br.length;i++) {
+      if (br.bytes[br.offset+i] != 0) {
+        return false;
+      }
+    }
+
+    return true;
+  }
+
   /** Creates a new deterministic, minimal automaton accepting
    *  all binary terms in the specified interval.  Note that unlike
    *  {@link #makeDecimalInterval}, the returned automaton is infinite,
@@ -238,17 +249,6 @@ final public class Automata {
       minInclusive = true;
     }
 
-    // Empty string corner cases:
-    if (max != null && maxInclusive == false && max.length == 1 && max.bytes[max.offset] == 0) {
-      max = new BytesRef();
-      maxInclusive = true;
-    }
-
-    if (min != null && minInclusive == false && min.length == 0) {
-      min = new BytesRef(new byte[1]);
-      minInclusive = true;
-    }
-
     int cmp;
     if (max != null) {
       cmp = min.compareTo(max);
@@ -270,8 +270,56 @@ final public class Automata {
       return makeEmpty();
     }
 
+    if (max != null &&
+        StringHelper.startsWith(max, min) &&
+        suffixIsZeros(max, min.length)) {
+
+      // Finite case: no sink state!
+
+      int maxLength = max.length;
+
+      // the == case was handled above
+      assert maxLength > min.length;
+
+      //  bar -> bar\0+
+      if (maxInclusive == false) {
+        maxLength--;
+      }
+
+      if (maxLength == min.length) {
+        if (minInclusive == false) {
+          return makeEmpty();
+        } else {
+          return makeBinary(min);
+        }
+      }
+
+      Automaton a = new Automaton();
+      int lastState = a.createState();
+      for (int i=0;i<min.length;i++) {
+        int state = a.createState();
+        int label = min.bytes[min.offset+i] & 0xff;
+        a.addTransition(lastState, state, label);
+        lastState = state;
+      }
+
+      if (minInclusive) {
+        a.setAccept(lastState, true);
+      }
+
+      for(int i=min.length;i<maxLength;i++) {
+        int state = a.createState();
+        a.addTransition(lastState, state, 0);
+        a.setAccept(state, true);
+        lastState = state;
+      }
+      a.finishState();
+      return a;
+    }
+
     Automaton a = new Automaton();
     int startState = a.createState();
+
     int sinkState = a.createState();
     a.setAccept(sinkState, true);
 
diff --git a/lucene/core/src/test/org/apache/lucene/util/automaton/TestAutomaton.java b/lucene/core/src/test/org/apache/lucene/util/automaton/TestAutomaton.java
index f291f450953..2d885d70f64 100644
--- a/lucene/core/src/test/org/apache/lucene/util/automaton/TestAutomaton.java
+++ b/lucene/core/src/test/org/apache/lucene/util/automaton/TestAutomaton.java
@@ -1105,6 +1105,145 @@ public class TestAutomaton extends LuceneTestCase {
     }
   }
 
+  private boolean accepts(Automaton a, BytesRef b) {
+    IntsRefBuilder intsBuilder = new IntsRefBuilder();
+    Util.toIntsRef(b, intsBuilder);    
+    return Operations.run(a, intsBuilder.toIntsRef());
+  }
+
+  private Automaton makeBinaryInterval(BytesRef minTerm, boolean minInclusive,
+                                       BytesRef maxTerm, boolean maxInclusive) {
+    
+    if (VERBOSE) {
+      System.out.println("TEST: minTerm=" + minTerm + " minInclusive=" + minInclusive + " maxTerm=" + maxTerm + " maxInclusive=" + maxInclusive);
+    }
+
+    Automaton a = Automata.makeBinaryInterval(minTerm, minInclusive,
+                                              maxTerm, maxInclusive);
+
+    Automaton minA = MinimizationOperations.minimize(a, Integer.MAX_VALUE);
+    if (minA.getNumStates() != a.getNumStates()) {
+      assertTrue(minA.getNumStates() < a.getNumStates());
+      System.out.println("Original was not minimal:");
+      System.out.println("Original:\n" + a.toDot());
+      System.out.println("Minimized:\n" + minA.toDot());
+      System.out.println("minTerm=" + minTerm + " minInclusive=" + minInclusive);
+      System.out.println("maxTerm=" + maxTerm + " maxInclusive=" + maxInclusive);
+      fail("automaton was not minimal");
+    }
+
+    if (VERBOSE) {
+      System.out.println(a.toDot());
+    }
+
+    return a;
+  }
+
+  public void testMakeBinaryIntervalFiniteCasesBasic() throws Exception {
+    // 0 (incl) - 00 (incl)
+    byte[] zeros = new byte[3];
+    Automaton a = makeBinaryInterval(new BytesRef(zeros, 0, 1), true, new BytesRef(zeros, 0, 2), true);
+    assertTrue(Operations.isFinite(a));
+    assertFalse(accepts(a, new BytesRef()));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 1)));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 2)));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 3)));
+
+    // '' (incl) - 00 (incl)
+    a = makeBinaryInterval(new BytesRef(), true, new BytesRef(zeros, 0, 2), true);
+    assertTrue(Operations.isFinite(a));
+    assertTrue(accepts(a, new BytesRef()));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 1)));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 2)));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 3)));
+
+    // '' (excl) - 00 (incl)
+    a = makeBinaryInterval(new BytesRef(), false, new BytesRef(zeros, 0, 2), true);
+    assertTrue(Operations.isFinite(a));
+    assertFalse(accepts(a, new BytesRef()));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 1)));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 2)));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 3)));
+
+    // 0 (excl) - 00 (incl)
+    a = makeBinaryInterval(new BytesRef(zeros, 0, 1), false, new BytesRef(zeros, 0, 2), true);
+    assertTrue(Operations.isFinite(a));
+    assertFalse(accepts(a, new BytesRef()));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 1)));
+    assertTrue(accepts(a, new BytesRef(zeros, 0, 2)));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 3)));
+
+    // 0 (excl) - 00 (excl)
+    a = makeBinaryInterval(new BytesRef(zeros, 0, 1), false, new BytesRef(zeros, 0, 2), false);
+    assertTrue(Operations.isFinite(a));
+    assertFalse(accepts(a, new BytesRef()));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 1)));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 2)));
+    assertFalse(accepts(a, new BytesRef(zeros, 0, 3)));
+  }
+
+  public void testMakeBinaryIntervalFiniteCasesRandom() throws Exception {
+    int iters = atLeast(100);
+    for(int iter=0;iter<iters;iter++) {
+      BytesRef prefix = new BytesRef(TestUtil.randomRealisticUnicodeString(random()));
+
+      BytesRefBuilder b = new BytesRefBuilder();
+      b.append(prefix);
+      int numZeros = random().nextInt(10);
+      for(int i=0;i<numZeros;i++) {
+        b.append((byte) 0);
+      }
+      BytesRef minTerm = b.get();
+
+      b = new BytesRefBuilder();
+      b.append(minTerm);
+      numZeros = random().nextInt(10);
+      for(int i=0;i<numZeros;i++) {
+        b.append((byte) 0);
+      }
+      BytesRef maxTerm = b.get();
+      
+      boolean minInclusive = random().nextBoolean();
+      boolean maxInclusive = random().nextBoolean();
+      Automaton a = makeBinaryInterval(minTerm, minInclusive,
+                                       maxTerm, maxInclusive);
+      assertTrue(Operations.isFinite(a));
+      int expectedCount = maxTerm.length - minTerm.length + 1;
+      if (minInclusive == false) {
+        expectedCount--;
+      }
+      if (maxInclusive == false) {
+        expectedCount--;
+      }
+
+      if (expectedCount <= 0) {
+        assertTrue(Operations.isEmpty(a));
+        continue;
+      } else {
+        // Enumerate all finite strings and verify the count matches what we expect:
+        assertEquals(expectedCount, Operations.getFiniteStrings(a, expectedCount).size());
+      }
+
+      b = new BytesRefBuilder();
+      b.append(minTerm);
+      if (minInclusive == false) {
+        assertFalse(accepts(a, b.get()));
+        b.append((byte) 0);
+      }
+      while (b.length() < maxTerm.length) {
+        b.append((byte) 0);
+
+        boolean expected;
+        if (b.length() == maxTerm.length) {
+          expected = maxInclusive;
+        } else {
+          expected = true;
+        }
+        assertEquals(expected, accepts(a, b.get()));
+      }
+    }
+  }
+
   public void testMakeBinaryIntervalRandom() throws Exception {
     int iters = atLeast(100);
     for(int iter=0;iter<iters;iter++) {
@@ -1113,26 +1252,7 @@ public class TestAutomaton extends LuceneTestCase {
       BytesRef maxTerm = TestUtil.randomBinaryTerm(random());
       boolean maxInclusive = random().nextBoolean();
 
-      if (VERBOSE) {
-        System.out.println("TEST: iter=" + iter + " minTerm=" + minTerm + " minInclusive=" + minInclusive + " maxTerm=" + maxTerm + " maxInclusive=" + maxInclusive);
-      }
-
-      Automaton a = Automata.makeBinaryInterval(minTerm, minInclusive, maxTerm, maxInclusive);
-
-      Automaton minA = MinimizationOperations.minimize(a, Integer.MAX_VALUE);
-      if (minA.getNumStates() != a.getNumStates()) {
-        assertTrue(minA.getNumStates() < a.getNumStates());
-        System.out.println("Original was not minimal:");
-        System.out.println("Original:\n" + a.toDot());
-        System.out.println("Minimized:\n" + minA.toDot());
-        System.out.println("minTerm=" + minTerm + " minInclusive=" + minInclusive);
-        System.out.println("maxTerm=" + maxTerm + " maxInclusive=" + maxInclusive);
-        fail("automaton was not minimal");
-      }
-
-      if (VERBOSE) {
-        System.out.println(a.toDot());
-      }
+      Automaton a = makeBinaryInterval(minTerm, minInclusive, maxTerm, maxInclusive);
 
       for(int iter2=0;iter2<500;iter2++) {
         BytesRef term = TestUtil.randomBinaryTerm(random());