diff --git a/qa/build.gradle b/qa/build.gradle
index 494f6e3cd94b7..709c309359ecf 100644
--- a/qa/build.gradle
+++ b/qa/build.gradle
@@ -4,7 +4,7 @@ import org.elasticsearch.gradle.test.RestIntegTestTask
 subprojects { Project subproj ->
   subproj.tasks.withType(RestIntegTestTask) {
     subproj.extensions.configure("${it.name}Cluster") { cluster ->
-      cluster.distribution = 'oss-zip'
+      cluster.distribution = System.getProperty('tests.distribution', 'oss-zip')
     }
   }
 }
diff --git a/qa/mixed-cluster/build.gradle b/qa/mixed-cluster/build.gradle
index d335ac982fd8a..da99bbb4c8036 100644
--- a/qa/mixed-cluster/build.gradle
+++ b/qa/mixed-cluster/build.gradle
@@ -54,9 +54,16 @@ for (Version version : bwcVersions.wireCompatible) {
     bwcTest.dependsOn(versionBwcTest)
   }
 
-  /* To support taking index snapshots, we have to set path.repo setting */
   tasks.getByName("${baseName}#mixedClusterTestRunner").configure {
+    /* To support taking index snapshots, we have to set path.repo setting */
     systemProperty 'tests.path.repo', new File(buildDir, "cluster/shared/repo")
+    if ('zip'.equals(extension.distribution)) {
+      systemProperty 'tests.rest.blacklist', [
+          'cat.templates/10_basic/No templates',
+          'cat.templates/10_basic/Sort templates',
+          'cat.templates/10_basic/Multiple template',
+        ].join(',')
+    }
   }
 }
 
diff --git a/qa/smoke-test-multinode/build.gradle b/qa/smoke-test-multinode/build.gradle
index 5df77bd0d9513..9d299e16f0210 100644
--- a/qa/smoke-test-multinode/build.gradle
+++ b/qa/smoke-test-multinode/build.gradle
@@ -27,3 +27,13 @@ integTest {
 integTestCluster {
   numNodes = 2
 }
+
+integTestRunner {
+  if ('zip'.equals(integTestCluster.distribution)) {
+    systemProperty 'tests.rest.blacklist', [
+        'cat.templates/10_basic/No templates',
+        'cat.templates/10_basic/Sort templates',
+        'cat.templates/10_basic/Multiple template',
+      ].join(',')
+  }
+}
diff --git a/qa/smoke-test-rank-eval-with-mustache/build.gradle b/qa/smoke-test-rank-eval-with-mustache/build.gradle
index 7274e65f4e1bd..122c2603719a0 100644
--- a/qa/smoke-test-rank-eval-with-mustache/build.gradle
+++ b/qa/smoke-test-rank-eval-with-mustache/build.gradle
@@ -26,3 +26,11 @@ dependencies {
     testCompile project(path: ':modules:lang-mustache', configuration: 'runtime')
 }
 
+/*
+ * One of the integration tests doesn't work with the zip distribution
+ * and will be fixed later.
+ * Tracked by https://github.com/elastic/elasticsearch/issues/30628
+ */
+if ("zip".equals(integTestCluster.distribution)) {
+    integTestRunner.enabled = false
+}
diff --git a/test/framework/src/main/java/org/elasticsearch/test/junit/listeners/ReproduceInfoPrinter.java b/test/framework/src/main/java/org/elasticsearch/test/junit/listeners/ReproduceInfoPrinter.java
index ca16ac6204a90..877a6f2e98a67 100644
--- a/test/framework/src/main/java/org/elasticsearch/test/junit/listeners/ReproduceInfoPrinter.java
+++ b/test/framework/src/main/java/org/elasticsearch/test/junit/listeners/ReproduceInfoPrinter.java
@@ -149,6 +149,7 @@ public ReproduceErrorMessageBuilder appendESProperties() {
             }
             appendOpt("tests.locale", Locale.getDefault().toLanguageTag());
             appendOpt("tests.timezone", TimeZone.getDefault().getID());
+            appendOpt("tests.distribution", System.getProperty("tests.distribution"));
             return this;
         }