diff --git a/server/src/main/java/org/elasticsearch/Version.java b/server/src/main/java/org/elasticsearch/Version.java
index 5a921098b4c..0f636f76d8a 100644
--- a/server/src/main/java/org/elasticsearch/Version.java
+++ b/server/src/main/java/org/elasticsearch/Version.java
@@ -107,6 +107,8 @@ public class Version implements Comparable<Version>, ToXContentFragment {
     public static final Version V_6_4_3 = new Version(V_6_4_3_ID, org.apache.lucene.util.Version.LUCENE_7_4_0);
     public static final int V_6_5_0_ID = 6050099;
     public static final Version V_6_5_0 = new Version(V_6_5_0_ID, org.apache.lucene.util.Version.LUCENE_7_5_0);
+    public static final int V_6_6_0_ID = 6060099;
+    public static final Version V_6_6_0 = new Version(V_6_6_0_ID, org.apache.lucene.util.Version.LUCENE_7_5_0);
     public static final int V_7_0_0_alpha1_ID = 7000001;
     public static final Version V_7_0_0_alpha1 =
         new Version(V_7_0_0_alpha1_ID, org.apache.lucene.util.Version.LUCENE_8_0_0);
@@ -125,6 +127,8 @@ public class Version implements Comparable<Version>, ToXContentFragment {
         switch (id) {
             case V_7_0_0_alpha1_ID:
                 return V_7_0_0_alpha1;
+            case V_6_6_0_ID:
+                return V_6_6_0;
             case V_6_5_0_ID:
                 return V_6_5_0;
             case V_6_4_3_ID:
diff --git a/server/src/test/java/org/elasticsearch/VersionTests.java b/server/src/test/java/org/elasticsearch/VersionTests.java
index c0d29e86fd6..e1a7633e1d0 100644
--- a/server/src/test/java/org/elasticsearch/VersionTests.java
+++ b/server/src/test/java/org/elasticsearch/VersionTests.java
@@ -181,7 +181,7 @@ public class VersionTests extends ESTestCase {
 
         // from 7.0 on we are supporting the latest minor of the previous major... this might fail once we add a new version ie. 5.x is
         // released since we need to bump the supported minor in Version#minimumCompatibilityVersion()
-        Version lastVersion = Version.V_6_5_0; // TODO: remove this once min compat version is a constant instead of method
+        Version lastVersion = Version.V_6_6_0; // TODO: remove this once min compat version is a constant instead of method
         assertEquals(lastVersion.major, Version.V_7_0_0_alpha1.minimumCompatibilityVersion().major);
         assertEquals("did you miss to bump the minor in Version#minimumCompatibilityVersion()",
                 lastVersion.minor, Version.V_7_0_0_alpha1.minimumCompatibilityVersion().minor);
@@ -340,7 +340,8 @@ public class VersionTests extends ESTestCase {
 
     public void testIsCompatible() {
         assertTrue(isCompatible(Version.CURRENT, Version.CURRENT.minimumCompatibilityVersion()));
-        assertTrue(isCompatible(Version.V_6_5_0, Version.V_7_0_0_alpha1));
+        assertFalse(isCompatible(Version.V_6_5_0, Version.V_7_0_0_alpha1));
+        assertTrue(isCompatible(Version.V_6_6_0, Version.V_7_0_0_alpha1));
         assertFalse(isCompatible(Version.fromId(2000099), Version.V_7_0_0_alpha1));
         assertFalse(isCompatible(Version.fromId(2000099), Version.V_6_5_0));
         assertFalse(isCompatible(Version.fromString("7.0.0"), Version.fromString("8.0.0")));
diff --git a/server/src/test/java/org/elasticsearch/transport/TcpTransportTests.java b/server/src/test/java/org/elasticsearch/transport/TcpTransportTests.java
index c6fb1f406cf..a17103789f2 100644
--- a/server/src/test/java/org/elasticsearch/transport/TcpTransportTests.java
+++ b/server/src/test/java/org/elasticsearch/transport/TcpTransportTests.java
@@ -156,27 +156,29 @@ public class TcpTransportTests extends ESTestCase {
         TcpTransport.ensureVersionCompatibility(VersionUtils.randomVersionBetween(random(), Version.CURRENT.minimumCompatibilityVersion(),
             Version.CURRENT), Version.CURRENT, randomBoolean());
 
-        TcpTransport.ensureVersionCompatibility(Version.fromString("6.0.0"), Version.fromString("7.0.0"), true);
+        final Version version = Version.fromString("7.0.0");
+        TcpTransport.ensureVersionCompatibility(Version.fromString("6.0.0"), version, true);
         IllegalStateException ise = expectThrows(IllegalStateException.class, () ->
-            TcpTransport.ensureVersionCompatibility(Version.fromString("6.0.0"), Version.fromString("7.0.0"), false));
-        assertEquals("Received message from unsupported version: [6.0.0] minimal compatible version is: [6.5.0]", ise.getMessage());
+            TcpTransport.ensureVersionCompatibility(Version.fromString("6.0.0"), version, false));
+        assertEquals("Received message from unsupported version: [6.0.0] minimal compatible version is: ["
+            + version.minimumCompatibilityVersion() + "]", ise.getMessage());
 
         // For handshake we are compatible with N-2
-        TcpTransport.ensureVersionCompatibility(Version.fromString("5.6.0"), Version.fromString("7.0.0"), true);
+        TcpTransport.ensureVersionCompatibility(Version.fromString("5.6.0"), version, true);
         ise = expectThrows(IllegalStateException.class, () ->
-            TcpTransport.ensureVersionCompatibility(Version.fromString("5.6.0"), Version.fromString("7.0.0"), false));
-        assertEquals("Received message from unsupported version: [5.6.0] minimal compatible version is: [6.5.0]",
-            ise.getMessage());
+            TcpTransport.ensureVersionCompatibility(Version.fromString("5.6.0"), version, false));
+        assertEquals("Received message from unsupported version: [5.6.0] minimal compatible version is: ["
+                + version.minimumCompatibilityVersion() + "]", ise.getMessage());
 
         ise = expectThrows(IllegalStateException.class, () ->
-            TcpTransport.ensureVersionCompatibility(Version.fromString("2.3.0"), Version.fromString("7.0.0"), true));
-        assertEquals("Received handshake message from unsupported version: [2.3.0] minimal compatible version is: [6.5.0]",
-            ise.getMessage());
+            TcpTransport.ensureVersionCompatibility(Version.fromString("2.3.0"), version, true));
+        assertEquals("Received handshake message from unsupported version: [2.3.0] minimal compatible version is: ["
+            + version.minimumCompatibilityVersion() + "]", ise.getMessage());
 
         ise = expectThrows(IllegalStateException.class, () ->
-            TcpTransport.ensureVersionCompatibility(Version.fromString("2.3.0"), Version.fromString("7.0.0"), false));
-        assertEquals("Received message from unsupported version: [2.3.0] minimal compatible version is: [6.5.0]",
-            ise.getMessage());
+            TcpTransport.ensureVersionCompatibility(Version.fromString("2.3.0"), version, false));
+        assertEquals("Received message from unsupported version: [2.3.0] minimal compatible version is: ["
+            + version.minimumCompatibilityVersion() + "]", ise.getMessage());
     }
 
     public void testCompressRequest() throws IOException {