diff --git a/solr/CHANGES.txt b/solr/CHANGES.txt
index e90d572eec6..d54063779ec 100644
--- a/solr/CHANGES.txt
+++ b/solr/CHANGES.txt
@@ -315,6 +315,8 @@ Other Changes
 * SOLR-7173: Fix ReplicationFactorTest on Windows by adding better retry
   support after seeing no response exceptions. (Ishan Chattopadhyaya via Timothy Potter)
 
+* SOLR-7246: Speed up BasicZkTest, TestManagedResourceStorage (Ramkumar Aiyengar)
+
 ==================  5.0.0 ==================
 
 Consult the LUCENE_CHANGES.txt file for additional, low level, changes in this release.
diff --git a/solr/test-framework/src/java/org/apache/solr/SolrTestCaseJ4.java b/solr/test-framework/src/java/org/apache/solr/SolrTestCaseJ4.java
index 078b75d59ab..ade905f1f61 100644
--- a/solr/test-framework/src/java/org/apache/solr/SolrTestCaseJ4.java
+++ b/solr/test-framework/src/java/org/apache/solr/SolrTestCaseJ4.java
@@ -55,6 +55,7 @@ import org.apache.solr.core.SolrConfig;
 import org.apache.solr.core.SolrCore;
 import org.apache.solr.core.SolrResourceLoader;
 import org.apache.solr.core.SolrXmlConfig;
+import org.apache.solr.core.ZkContainer;
 import org.apache.solr.handler.UpdateRequestHandler;
 import org.apache.solr.request.LocalSolrQueryRequest;
 import org.apache.solr.request.SolrQueryRequest;
@@ -68,6 +69,7 @@ import org.apache.solr.util.AbstractSolrTestCase;
 import org.apache.solr.util.RevertDefaultThreadHandlerRule;
 import org.apache.solr.util.SSLTestConfig;
 import org.apache.solr.util.TestHarness;
+import org.apache.zookeeper.KeeperException;
 import org.junit.AfterClass;
 import org.junit.BeforeClass;
 import org.junit.ClassRule;
@@ -686,7 +688,21 @@ public abstract class SolrTestCaseJ4 extends LuceneTestCase {
    */
   public static void deleteCore() {
     log.info("###deleteCore" );
-    if (h != null) { h.close(); }
+    if (h != null) {
+      // If the test case set up Zk, it should still have it as available,
+      // otherwise the core close will just be unnecessarily delayed.
+      CoreContainer cc = h.getCoreContainer();
+      if (! cc.getCores().isEmpty() && cc.isZooKeeperAware()) {
+        try {
+          cc.getZkController().getZkClient().exists("/", false);
+        } catch (KeeperException e) {
+          log.error("Testing connectivity to ZK by checking for root path failed", e);
+          fail("Trying to tear down a ZK aware core container with ZK not reachable");
+        } catch (InterruptedException ignored) {}
+      }
+
+      h.close();
+    }
 
     if (factoryProp == null) {
       System.clearProperty("solr.directoryFactory");
diff --git a/solr/test-framework/src/java/org/apache/solr/cloud/AbstractZkTestCase.java b/solr/test-framework/src/java/org/apache/solr/cloud/AbstractZkTestCase.java
index 382d3d497d1..c317c9b2b8a 100644
--- a/solr/test-framework/src/java/org/apache/solr/cloud/AbstractZkTestCase.java
+++ b/solr/test-framework/src/java/org/apache/solr/cloud/AbstractZkTestCase.java
@@ -147,6 +147,8 @@ public abstract class AbstractZkTestCase extends SolrTestCaseJ4 {
   
   @AfterClass
   public static void azt_afterClass() throws Exception {
+    deleteCore();
+
     System.clearProperty("zkHost");
     System.clearProperty("solr.test.sys.prop1");
     System.clearProperty("solr.test.sys.prop2");