diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index a3dc9d595f1f..e60f2b1a5540 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -188,7 +188,9 @@ Improvements
 
 Optimizations
 ---------------------
-(No changes)
+
+* GITHUB#12839: Introduce method to grow arrays up to a given upper limit and use it to reduce overallocation for
+  DirectoryTaxonomyReader#getBulkOrdinals. (Stefan Vodita)
 
 Bug Fixes
 ---------------------
diff --git a/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java b/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java
index 629e289ef4db..336b5b3e6bbb 100644
--- a/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java
+++ b/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java
@@ -330,15 +330,36 @@ public static int[] growExact(int[] array, int newLength) {
     return copy;
   }
 
+  /**
+   * Returns an array whose size is at least {@code minLength}, generally over-allocating
+   * exponentially, but never allocating more than {@code maxLength} elements.
+   */
+  public static int[] growInRange(int[] array, int minLength, int maxLength) {
+    assert minLength >= 0
+        : "length must be positive (got " + minLength + "): likely integer overflow?";
+
+    if (minLength > maxLength) {
+      throw new IllegalArgumentException(
+          "requested minimum array length "
+              + minLength
+              + " is larger than requested maximum array length "
+              + maxLength);
+    }
+
+    if (array.length >= minLength) {
+      return array;
+    }
+
+    int potentialLength = oversize(minLength, Integer.BYTES);
+    return growExact(array, Math.min(maxLength, potentialLength));
+  }
+
   /**
    * Returns an array whose size is at least {@code minSize}, generally over-allocating
    * exponentially
    */
   public static int[] grow(int[] array, int minSize) {
-    assert minSize >= 0 : "size must be positive (got " + minSize + "): likely integer overflow?";
-    if (array.length < minSize) {
-      return growExact(array, oversize(minSize, Integer.BYTES));
-    } else return array;
+    return growInRange(array, minSize, Integer.MAX_VALUE);
   }
 
   /**
diff --git a/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java b/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java
index abc41a5bf9fa..972fd0c3c848 100644
--- a/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java
+++ b/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java
@@ -18,6 +18,8 @@
 
 import static org.apache.lucene.util.ArrayUtil.copyOfSubArray;
 import static org.apache.lucene.util.ArrayUtil.growExact;
+import static org.apache.lucene.util.ArrayUtil.growInRange;
+import static org.apache.lucene.util.ArrayUtil.oversize;
 
 import java.util.Arrays;
 import java.util.Collections;
@@ -371,6 +373,36 @@ public void testGrowExact() {
         () -> growExact(new String[] {"a", "b", "c"}, random().nextInt(3)));
   }
 
+  public void testGrowInRange() {
+    int[] array = new int[] {1, 2, 3};
+
+    // If minLength is negative, maxLength does not matter
+    expectThrows(AssertionError.class, () -> growInRange(array, -1, 4));
+    expectThrows(AssertionError.class, () -> growInRange(array, -1, 0));
+    expectThrows(AssertionError.class, () -> growInRange(array, -1, -1));
+
+    // If minLength > maxLength, we throw an exception
+    expectThrows(IllegalArgumentException.class, () -> growInRange(array, 1, 0));
+    expectThrows(IllegalArgumentException.class, () -> growInRange(array, 4, 3));
+    expectThrows(IllegalArgumentException.class, () -> growInRange(array, 5, 4));
+
+    // If minLength is sufficient, we return the array
+    assertSame(array, growInRange(array, 1, 4));
+    assertSame(array, growInRange(array, 1, 2));
+    assertSame(array, growInRange(array, 1, 1));
+
+    int minLength = 4;
+    int maxLength = Integer.MAX_VALUE;
+
+    // The array grows normally if maxLength permits
+    assertEquals(
+        oversize(minLength, Integer.BYTES),
+        growInRange(new int[] {1, 2, 3}, minLength, maxLength).length);
+
+    // The array grows to maxLength if maxLength is limiting
+    assertEquals(minLength, growInRange(new int[] {1, 2, 3}, minLength, minLength).length);
+  }
+
   public void testCopyOfSubArray() {
     short[] shortArray = {1, 2, 3};
     assertArrayEquals(new short[] {1}, copyOfSubArray(shortArray, 0, 1));
diff --git a/lucene/facet/src/java/org/apache/lucene/facet/taxonomy/directory/DirectoryTaxonomyReader.java b/lucene/facet/src/java/org/apache/lucene/facet/taxonomy/directory/DirectoryTaxonomyReader.java
index bf4867e0dda8..0d641d396ec8 100644
--- a/lucene/facet/src/java/org/apache/lucene/facet/taxonomy/directory/DirectoryTaxonomyReader.java
+++ b/lucene/facet/src/java/org/apache/lucene/facet/taxonomy/directory/DirectoryTaxonomyReader.java
@@ -328,7 +328,8 @@ public int[] getBulkOrdinals(FacetLabel... categoryPaths) throws IOException {
     }
     // First try to find results in the cache:
     int[] result = new int[categoryPaths.length];
-    int[] indexesMissingFromCache = new int[10]; // initial size, will grow when required
+    // Will grow when required, but never beyond categoryPaths.length
+    int[] indexesMissingFromCache = new int[Math.min(10, categoryPaths.length)];
     int numberOfMissingFromCache = 0;
     FacetLabel cp;
     Integer res;
@@ -352,7 +353,8 @@ public int[] getBulkOrdinals(FacetLabel... categoryPaths) throws IOException {
         }
       } else {
         indexesMissingFromCache =
-            ArrayUtil.grow(indexesMissingFromCache, numberOfMissingFromCache + 1);
+            ArrayUtil.growInRange(
+                indexesMissingFromCache, numberOfMissingFromCache + 1, categoryPaths.length);
         indexesMissingFromCache[numberOfMissingFromCache++] = i;
       }
     }