diff --git a/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedEagerOnBothSidesIT.java b/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedEagerOnBothSidesIT.java
index fed962af754..cd26eba88b1 100644
--- a/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedEagerOnBothSidesIT.java
+++ b/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedEagerOnBothSidesIT.java
@@ -6,8 +6,6 @@
  */
 package org.hibernate.search.integrationtest.mapper.orm.automaticindexing.association.bytype.onetoone.ownedbycontained;
 
-import static org.junit.Assume.assumeTrue;
-
 import java.util.ArrayList;
 import java.util.List;
 import java.util.Optional;
@@ -94,46 +92,6 @@ public void setup(OrmSetupHelper.SetupContext setupContext,
 		} );
 	}
 
-	@Override
-	public void directAssociationUpdate_indexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void directAssociationUpdate_indexedEmbeddedShallowReindexOnUpdate() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void directAssociationUpdate_embeddedAssociationsIndexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_indexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_indexedEmbeddedShallowReindexOnUpdate() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_usedInCrossEntityDerivedProperty() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_embeddedAssociationsIndexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	private void notTestedBecauseOfHSEARCH4305AndHSEARCH4708() {
-		assumeTrue( "Association update tests fail because of https://hibernate.atlassian.net/browse/HSEARCH-4305 / https://hibernate.atlassian.net/browse/HSEARCH-4708",
-				false );
-	}
-
 	@Entity(name = "containing")
 	public static class ContainingEntity {
 
diff --git a/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainedSideIT.java b/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainedSideIT.java
index c83951edd26..4c6935f2031 100644
--- a/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainedSideIT.java
+++ b/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainedSideIT.java
@@ -6,8 +6,6 @@
  */
 package org.hibernate.search.integrationtest.mapper.orm.automaticindexing.association.bytype.onetoone.ownedbycontained;
 
-import static org.junit.Assume.assumeTrue;
-
 import java.util.ArrayList;
 import java.util.List;
 import java.util.Optional;
@@ -98,46 +96,6 @@ public void setup(OrmSetupHelper.SetupContext setupContext,
 		} );
 	}
 
-	@Override
-	public void directAssociationUpdate_indexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void directAssociationUpdate_indexedEmbeddedShallowReindexOnUpdate() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void directAssociationUpdate_embeddedAssociationsIndexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_indexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_indexedEmbeddedShallowReindexOnUpdate() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_usedInCrossEntityDerivedProperty() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_embeddedAssociationsIndexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	private void notTestedBecauseOfHSEARCH4305AndHSEARCH4708() {
-		assumeTrue( "Association update tests fail because of https://hibernate.atlassian.net/browse/HSEARCH-4305 / https://hibernate.atlassian.net/browse/HSEARCH-4708",
-				false );
-	}
-
 	@Entity(name = "containing")
 	public static class ContainingEntity {
 
diff --git a/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainingSideIT.java b/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainingSideIT.java
index 2e26222279f..ea1a91f177a 100644
--- a/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainingSideIT.java
+++ b/integrationtest/mapper/orm/src/test/java/org/hibernate/search/integrationtest/mapper/orm/automaticindexing/association/bytype/onetoone/ownedbycontained/AutomaticIndexingOneToOneOwnedByContainedLazyOnContainingSideIT.java
@@ -6,8 +6,6 @@
  */
 package org.hibernate.search.integrationtest.mapper.orm.automaticindexing.association.bytype.onetoone.ownedbycontained;
 
-import static org.junit.Assume.assumeTrue;
-
 import java.util.ArrayList;
 import java.util.List;
 import java.util.Optional;
@@ -98,46 +96,6 @@ public void setup(OrmSetupHelper.SetupContext setupContext,
 		} );
 	}
 
-	@Override
-	public void directAssociationUpdate_indexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void directAssociationUpdate_indexedEmbeddedShallowReindexOnUpdate() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void directAssociationUpdate_embeddedAssociationsIndexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_indexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_indexedEmbeddedShallowReindexOnUpdate() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_usedInCrossEntityDerivedProperty() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	@Override
-	public void indirectAssociationUpdate_embeddedAssociationsIndexedEmbedded() {
-		notTestedBecauseOfHSEARCH4305AndHSEARCH4708();
-	}
-
-	private void notTestedBecauseOfHSEARCH4305AndHSEARCH4708() {
-		assumeTrue( "Association update tests fail because of https://hibernate.atlassian.net/browse/HSEARCH-4305 / https://hibernate.atlassian.net/browse/HSEARCH-4708",
-				false );
-	}
-
 	@Entity(name = "containing")
 	public static class ContainingEntity {