diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index 29ad1294e40..721efe54289 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -142,6 +142,9 @@ Optimizations
 * LUCENE-7396, LUCENE-7399: Faster flush of points.
   (Adrien Grand, Mike McCandless)
 
+* LUCENE-7406: Automaton and PrefixQuery tweaks (fewer object (re)allocations).
+  (Christine Poerschke)
+
 Other
 
 * LUCENE-4787: Fixed some highlighting javadocs. (Michael Dodsworth via Adrien
diff --git a/lucene/core/src/java/org/apache/lucene/search/PrefixQuery.java b/lucene/core/src/java/org/apache/lucene/search/PrefixQuery.java
index f4b5e5026cf..84ae8deae6f 100644
--- a/lucene/core/src/java/org/apache/lucene/search/PrefixQuery.java
+++ b/lucene/core/src/java/org/apache/lucene/search/PrefixQuery.java
@@ -41,7 +41,8 @@ public class PrefixQuery extends AutomatonQuery {
 
   /** Build an automaton accepting all terms with the specified prefix. */
   public static Automaton toAutomaton(BytesRef prefix) {
-    Automaton automaton = new Automaton();
+    final int numStatesAndTransitions = prefix.length+1;
+    final Automaton automaton = new Automaton(numStatesAndTransitions, numStatesAndTransitions);
     int lastState = automaton.createState();
     for(int i=0;i<prefix.length;i++) {
       int state = automaton.createState();
@@ -66,7 +67,7 @@ public class PrefixQuery extends AutomatonQuery {
     StringBuilder buffer = new StringBuilder();
     if (!getField().equals(field)) {
       buffer.append(getField());
-      buffer.append(":");
+      buffer.append(':');
     }
     buffer.append(term.text());
     buffer.append('*');
diff --git a/lucene/core/src/java/org/apache/lucene/util/automaton/Automaton.java b/lucene/core/src/java/org/apache/lucene/util/automaton/Automaton.java
index 42f28edacb0..0dd449c9961 100644
--- a/lucene/core/src/java/org/apache/lucene/util/automaton/Automaton.java
+++ b/lucene/core/src/java/org/apache/lucene/util/automaton/Automaton.java
@@ -357,13 +357,13 @@ public class Automaton implements Accountable {
   }
 
   private void growStates() {
-    if (nextState+2 >= states.length) {
+    if (nextState+2 > states.length) {
       states = ArrayUtil.grow(states, nextState+2);
     }
   }
 
   private void growTransitions() {
-    if (nextTransition+3 >= transitions.length) {
+    if (nextTransition+3 > transitions.length) {
       transitions = ArrayUtil.grow(transitions, nextTransition+3);
     }
   }