diff --git a/solr/CHANGES.txt b/solr/CHANGES.txt
index a5f4baf6e35..4d4754f0911 100644
--- a/solr/CHANGES.txt
+++ b/solr/CHANGES.txt
@@ -273,6 +273,8 @@ Optimizations
 
 * SOLR-4815: Admin-UI - DIH: Let "commit" be checked by default (steffkes)
 
+* SOLR-5002: optimize numDocs(Query,DocSet) when filterCache is null (Robert Muir)
+
 Other Changes
 ----------------------
 
diff --git a/solr/core/src/java/org/apache/solr/search/SolrIndexSearcher.java b/solr/core/src/java/org/apache/solr/search/SolrIndexSearcher.java
index 24e4290b3b2..02c768a5947 100644
--- a/solr/core/src/java/org/apache/solr/search/SolrIndexSearcher.java
+++ b/solr/core/src/java/org/apache/solr/search/SolrIndexSearcher.java
@@ -59,7 +59,10 @@ import org.apache.lucene.index.StoredFieldVisitor;
 import org.apache.lucene.index.Term;
 import org.apache.lucene.index.Terms;
 import org.apache.lucene.index.TermsEnum;
+import org.apache.lucene.search.BooleanClause;
+import org.apache.lucene.search.BooleanQuery;
 import org.apache.lucene.search.Collector;
+import org.apache.lucene.search.ConstantScoreQuery;
 import org.apache.lucene.search.DocIdSet;
 import org.apache.lucene.search.DocIdSetIterator;
 import org.apache.lucene.search.Explanation;
@@ -77,6 +80,7 @@ import org.apache.lucene.search.TopDocs;
 import org.apache.lucene.search.TopDocsCollector;
 import org.apache.lucene.search.TopFieldCollector;
 import org.apache.lucene.search.TopScoreDocCollector;
+import org.apache.lucene.search.TotalHitCountCollector;
 import org.apache.lucene.search.Weight;
 import org.apache.lucene.store.Directory;
 import org.apache.lucene.util.Bits;
@@ -1921,10 +1925,22 @@ public class SolrIndexSearcher extends IndexSearcher implements Closeable,SolrIn
    * @throws IOException If there is a low-level I/O error.
    */
   public int numDocs(Query a, DocSet b) throws IOException {
-    // Negative query if absolute value different from original
-    Query absQ = QueryUtils.getAbs(a);
-    DocSet positiveA = getPositiveDocSet(absQ);
-    return a==absQ ? b.intersectionSize(positiveA) : b.andNotSize(positiveA);
+    if (filterCache != null) {
+      // Negative query if absolute value different from original
+      Query absQ = QueryUtils.getAbs(a);
+      DocSet positiveA = getPositiveDocSet(absQ);
+      return a==absQ ? b.intersectionSize(positiveA) : b.andNotSize(positiveA);
+    } else {
+      // If there isn't a cache, then do a single filtered query
+      // NOTE: we cannot use FilteredQuery, because BitDocSet assumes it will never 
+      // have deleted documents, but UninvertedField's doNegative has sets with deleted docs
+      TotalHitCountCollector collector = new TotalHitCountCollector();
+      BooleanQuery bq = new BooleanQuery();
+      bq.add(QueryUtils.makeQueryable(a), BooleanClause.Occur.MUST);
+      bq.add(new ConstantScoreQuery(b.getTopFilter()), BooleanClause.Occur.MUST);
+      super.search(bq, null, collector);
+      return collector.getTotalHits();
+    }
   }
 
   /** @lucene.internal */