diff --git a/server/src/main/java/org/elasticsearch/search/aggregations/bucket/significant/GlobalOrdinalsSignificantTermsAggregator.java b/server/src/main/java/org/elasticsearch/search/aggregations/bucket/significant/GlobalOrdinalsSignificantTermsAggregator.java
index 66b8f8d5b15ed..25f83caa3eb92 100644
--- a/server/src/main/java/org/elasticsearch/search/aggregations/bucket/significant/GlobalOrdinalsSignificantTermsAggregator.java
+++ b/server/src/main/java/org/elasticsearch/search/aggregations/bucket/significant/GlobalOrdinalsSignificantTermsAggregator.java
@@ -20,10 +20,8 @@
 
 import org.apache.lucene.index.IndexReader;
 import org.apache.lucene.index.LeafReaderContext;
-import org.apache.lucene.index.SortedSetDocValues;
 import org.apache.lucene.util.BytesRef;
 import org.elasticsearch.common.lease.Releasables;
-import org.elasticsearch.common.util.LongHash;
 import org.elasticsearch.search.DocValueFormat;
 import org.elasticsearch.search.aggregations.Aggregator;
 import org.elasticsearch.search.aggregations.AggregatorFactories;
@@ -103,11 +101,22 @@ public SignificantStringTerms buildAggregation(long owningBucketOrdinal) throws
 
         BucketSignificancePriorityQueue<SignificantStringTerms.Bucket> ordered = new BucketSignificancePriorityQueue<>(size);
         SignificantStringTerms.Bucket spare = null;
-        for (long globalTermOrd = 0; globalTermOrd < valueCount; ++globalTermOrd) {
-            if (includeExclude != null && !acceptedGlobalOrdinals.get(globalTermOrd)) {
+        final boolean needsFullScan = bucketOrds == null || bucketCountThresholds.getMinDocCount() == 0;
+        final long maxId = needsFullScan ? valueCount : bucketOrds.size();
+        for (long ord = 0; ord < maxId; ord++) {
+            final long globalOrd;
+            final long bucketOrd;
+            if (needsFullScan) {
+                bucketOrd = bucketOrds == null ? ord : bucketOrds.find(ord);
+                globalOrd = ord;
+            } else {
+                assert bucketOrds != null;
+                bucketOrd = ord;
+                globalOrd = bucketOrds.get(ord);
+            }
+            if (includeExclude != null && !acceptedGlobalOrdinals.get(globalOrd)) {
                 continue;
             }
-            final long bucketOrd = getBucketOrd(globalTermOrd);
             final int bucketDocCount = bucketOrd < 0 ? 0 : bucketDocCount(bucketOrd);
             if (bucketCountThresholds.getMinDocCount() > 0 && bucketDocCount == 0) {
                 continue;
@@ -120,7 +129,7 @@ public SignificantStringTerms buildAggregation(long owningBucketOrdinal) throws
                 spare = new SignificantStringTerms.Bucket(new BytesRef(), 0, 0, 0, 0, null, format);
             }
             spare.bucketOrd = bucketOrd;
-            copy(lookupGlobalOrd.apply(globalTermOrd), spare.termBytes);
+            copy(lookupGlobalOrd.apply(globalOrd), spare.termBytes);
             spare.subsetDf = bucketDocCount;
             spare.subsetSize = subsetSize;
             spare.supersetDf = termsAggFactory.getBackgroundFrequency(spare.termBytes);
diff --git a/server/src/main/java/org/elasticsearch/search/aggregations/bucket/terms/GlobalOrdinalsStringTermsAggregator.java b/server/src/main/java/org/elasticsearch/search/aggregations/bucket/terms/GlobalOrdinalsStringTermsAggregator.java
index 6ad14b8d0f93a..03eb00337e9c1 100644
--- a/server/src/main/java/org/elasticsearch/search/aggregations/bucket/terms/GlobalOrdinalsStringTermsAggregator.java
+++ b/server/src/main/java/org/elasticsearch/search/aggregations/bucket/terms/GlobalOrdinalsStringTermsAggregator.java
@@ -71,7 +71,7 @@ public class GlobalOrdinalsStringTermsAggregator extends AbstractStringTermsAggr
     protected final long valueCount;
     protected final GlobalOrdLookupFunction lookupGlobalOrd;
 
-    private final LongHash bucketOrds;
+    protected final LongHash bucketOrds;
 
     public interface GlobalOrdLookupFunction {
         BytesRef apply(long ord) throws IOException;
@@ -107,10 +107,6 @@ boolean remapGlobalOrds() {
         return bucketOrds != null;
     }
 
-    protected final long getBucketOrd(long globalOrd) {
-        return bucketOrds == null ? globalOrd : bucketOrds.find(globalOrd);
-    }
-
     private void collectGlobalOrd(int doc, long globalOrd, LeafBucketCollector sub) throws IOException {
         if (bucketOrds == null) {
             collectExistingBucket(sub, doc, globalOrd);
@@ -188,17 +184,28 @@ public InternalAggregation buildAggregation(long owningBucketOrdinal) throws IOE
         long otherDocCount = 0;
         BucketPriorityQueue<OrdBucket> ordered = new BucketPriorityQueue<>(size, order.comparator(this));
         OrdBucket spare = new OrdBucket(-1, 0, null, showTermDocCountError, 0);
-        for (long globalTermOrd = 0; globalTermOrd < valueCount; ++globalTermOrd) {
-            if (includeExclude != null && !acceptedGlobalOrdinals.get(globalTermOrd)) {
+        final boolean needsFullScan = bucketOrds == null || bucketCountThresholds.getMinDocCount() == 0;
+        final long maxId = needsFullScan ? valueCount : bucketOrds.size();
+        for (long ord = 0; ord < maxId; ord++) {
+            final long globalOrd;
+            final long bucketOrd;
+            if (needsFullScan) {
+                bucketOrd = bucketOrds == null ? ord : bucketOrds.find(ord);
+                globalOrd = ord;
+            } else {
+                assert bucketOrds != null;
+                bucketOrd = ord;
+                globalOrd = bucketOrds.get(ord);
+            }
+            if (includeExclude != null && !acceptedGlobalOrdinals.get(globalOrd)) {
                 continue;
             }
-            final long bucketOrd = getBucketOrd(globalTermOrd);
             final int bucketDocCount = bucketOrd < 0 ? 0 : bucketDocCount(bucketOrd);
             if (bucketCountThresholds.getMinDocCount() > 0 && bucketDocCount == 0) {
                 continue;
             }
             otherDocCount += bucketDocCount;
-            spare.globalOrd = globalTermOrd;
+            spare.globalOrd = globalOrd;
             spare.bucketOrd = bucketOrd;
             spare.docCount = bucketDocCount;
             if (bucketCountThresholds.getShardMinDocCount() <= spare.docCount) {
@@ -378,7 +385,7 @@ private void mapSegmentCountsToGlobalCounts(LongUnaryOperator mapping) throws IO
                 }
                 final long ord = i - 1; // remember we do +1 when counting
                 final long globalOrd = mapping.applyAsLong(ord);
-                long bucketOrd = getBucketOrd(globalOrd);
+                long bucketOrd = bucketOrds == null ? globalOrd : bucketOrds.find(globalOrd);
                 incrementBucketDocCount(bucketOrd, inc);
             }
         }