diff --git a/pkg/acceptance/adapter_test.go b/pkg/acceptance/adapter_test.go
index de3722439b1e..d4e61c22958c 100644
--- a/pkg/acceptance/adapter_test.go
+++ b/pkg/acceptance/adapter_test.go
@@ -49,6 +49,7 @@ func TestDockerCSharp(t *testing.T) {
 }
 
 func TestDockerJava(t *testing.T) {
+	skip.WithIssue(t, 58955, "flaky test")
 	s := log.Scope(t)
 	defer s.Close(t)
 
@@ -69,6 +70,7 @@ func TestDockerElixir(t *testing.T) {
 }
 
 func TestDockerNodeJS(t *testing.T) {
+	skip.WithIssue(t, 58955, "flaky test")
 	s := log.Scope(t)
 	defer s.Close(t)
 
@@ -97,6 +99,7 @@ func TestDockerPHP(t *testing.T) {
 }
 
 func TestDockerPSQL(t *testing.T) {
+	skip.WithIssue(t, 58955, "flaky test")
 	s := log.Scope(t)
 	defer s.Close(t)
 
diff --git a/pkg/server/migration_test.go b/pkg/server/migration_test.go
index 42b79fad3703..76e8a08c1e70 100644
--- a/pkg/server/migration_test.go
+++ b/pkg/server/migration_test.go
@@ -23,6 +23,7 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/settings/cluster"
 	"github.com/cockroachdb/cockroach/pkg/testutils"
 	"github.com/cockroachdb/cockroach/pkg/testutils/serverutils"
+	"github.com/cockroachdb/cockroach/pkg/testutils/skip"
 	"github.com/cockroachdb/cockroach/pkg/util/leaktest"
 )
 
@@ -200,6 +201,7 @@ func TestBumpClusterVersion(t *testing.T) {
 
 func TestMigrationPurgeOutdatedReplicas(t *testing.T) {
 	defer leaktest.AfterTest(t)()
+	skip.WithIssue(t, 59180)
 
 	const numStores = 3
 	var storeSpecs []base.StoreSpec