diff --git a/pom.xml b/pom.xml
index bb9edb1213..68d11f6eb6 100644
--- a/pom.xml
+++ b/pom.xml
@@ -96,8 +96,7 @@
     <!-- Do not upgrade, leads to test failures, MSHARED-1014 -->
     <mavenSharedUtilsVersion>3.3.4</mavenSharedUtilsVersion>
     <powermockVersion>2.0.9</powermockVersion>
-    <!-- Do not upgrade, leads to test failures -->
-    <jacocoVersion>0.8.8</jacocoVersion>
+    <jacocoVersion>0.8.11</jacocoVersion>
     <testngVersion>5.11</testngVersion>
     <surefire-shared-utils.version>${project.version}</surefire-shared-utils.version>
     <maven.surefire.scm.devConnection>scm:git:https://gitbox.apache.org/repos/asf/maven-surefire.git</maven.surefire.scm.devConnection>
diff --git a/surefire-its/src/test/java/org/apache/maven/surefire/its/CheckTestNgVersionsIT.java b/surefire-its/src/test/java/org/apache/maven/surefire/its/CheckTestNgVersionsIT.java
index 557e13d11d..f008e7ee15 100644
--- a/surefire-its/src/test/java/org/apache/maven/surefire/its/CheckTestNgVersionsIT.java
+++ b/surefire-its/src/test/java/org/apache/maven/surefire/its/CheckTestNgVersionsIT.java
@@ -25,7 +25,6 @@
 import org.apache.maven.surefire.its.fixture.OutputValidator;
 import org.apache.maven.surefire.its.fixture.SurefireJUnit4IntegrationTestCase;
 import org.apache.maven.surefire.its.fixture.SurefireLauncher;
-import org.junit.Ignore;
 import org.junit.Test;
 
 import static org.junit.Assert.assertEquals;
@@ -41,106 +40,25 @@
  */
 public class CheckTestNgVersionsIT extends SurefireJUnit4IntegrationTestCase {
 
+    // TestNG 7.6 and above needs JDK11
     @Test
-    public void test47() {
-        runTestNgTest("4.7", "jdk15");
+    public void test751() {
+        runTestNgTestWithRunOrder("7.5.1");
     }
 
     @Test
-    @Ignore("5.0 and 5.0.1 jars on central are malformed SUREFIRE-375 + MAVENUPLOAD-1024")
-    public void xXXtest50() {
-        runTestNgTest("5.0", "jdk15");
+    public void test6143() {
+        runTestNgTestWithRunOrder("6.14.3");
     }
 
     @Test
-    @Ignore("5.0 and 5.0.1 jars on central are malformed SUREFIRE-375 + MAVENUPLOAD-1024")
-    public void xXXtest501() {
-        runTestNgTest("5.0.1", "jdk15");
+    public void test69136() {
+        runTestNgTestWithRunOrder("6.9.13.6");
     }
 
     @Test
-    public void test502() {
-        runTestNgTest("5.0.2", "jdk15");
-    }
-
-    @Test
-    public void test51() {
-        runTestNgTest("5.1", "jdk15");
-    }
-
-    @Test
-    public void test55() {
-        runTestNgTest("5.5", "jdk15");
-    }
-
-    @Test
-    public void test56() {
-        runTestNgTest("5.6", "jdk15");
-    }
-
-    @Test
-    public void test57() {
-        runTestNgTest("5.7", "jdk15");
-    }
-
-    @Test
-    public void test58() {
-        runTestNgTest("5.8", "jdk15");
-    }
-
-    @Test
-    public void test59() {
-        runTestNgTest("5.9", "jdk15");
-    }
-
-    @Test
-    public void test510() {
-        runTestNgTest("5.10", "jdk15");
-    }
-
-    @Test
-    public void test511() {
-        runTestNgTest("5.11", "jdk15");
-    }
-
-    @Test
-    public void test512() {
-        runTestNgTest("5.12.1");
-    }
-
-    @Test
-    public void test513() {
-        runTestNgTest("5.13");
-    }
-
-    @Test
-    public void test5131() {
-        runTestNgTest("5.13.1");
-    }
-
-    @Test
-    public void test514() {
-        runTestNgTest("5.14");
-    }
-
-    @Test
-    public void test5141() {
-        runTestNgTest("5.14.1");
-    }
-
-    @Test
-    public void test5142() {
-        runTestNgTest("5.14.2");
-    }
-
-    @Test
-    public void test60() {
-        runTestNgTest("6.0");
-    }
-
-    @Test
-    public void test685() {
-        runTestNgTestWithRunOrder("6.8.5");
+    public void test6821() {
+        runTestNgTestWithRunOrder("6.8.21");
     }
 
     private void runTestNgTestWithRunOrder(String version) {
diff --git a/surefire-its/src/test/java/org/apache/maven/surefire/its/jiras/Surefire1967CheckTestNgMethodParallelOrderingIT.java b/surefire-its/src/test/java/org/apache/maven/surefire/its/jiras/Surefire1967CheckTestNgMethodParallelOrderingIT.java
index 5a8ee476f7..0d41205d29 100644
--- a/surefire-its/src/test/java/org/apache/maven/surefire/its/jiras/Surefire1967CheckTestNgMethodParallelOrderingIT.java
+++ b/surefire-its/src/test/java/org/apache/maven/surefire/its/jiras/Surefire1967CheckTestNgMethodParallelOrderingIT.java
@@ -21,8 +21,6 @@
 import org.apache.maven.surefire.its.fixture.SurefireJUnit4IntegrationTestCase;
 import org.junit.Test;
 
-import static org.apache.maven.surefire.its.fixture.HelperAssertions.assumeJavaMaxVersion;
-
 /**
  * Test TestNG setup and teardown ordering with parallelism
  *
@@ -58,19 +56,4 @@ public void testNgParallelOrderingWithEarlyVersion6() {
                 .executeTest()
                 .verifyErrorFree(12);
     }
-
-    // TestNG 5.13+ already has XmlClass.m_index field, but doesn't have XmlClass.setIndex method.
-    // Note that the problem of wrong setup methods ordering (SUREFIRE-1967) was not observed on that version.
-    // This is likely because SUREFIRE-1967 is related to a change in TestNG 6.3, where preserve-order became true by
-    // default (https://github.com/cbeust/testng/commit/8849b3406ef2184ceb6002768a2d087d7a8de8d5).
-    @Test
-    public void testNgParallelOrderingWithVersion5() {
-        // TestNG 5.13 does not work with Java 17
-        assumeJavaMaxVersion(16);
-
-        unpack("surefire-1967-testng-method-parallel-ordering")
-                .sysProp("testNgVersion", "5.13")
-                .executeTest()
-                .verifyErrorFree(12);
-    }
 }