diff --git a/pkg/services/ngalert/notifier/alertmanager_test.go b/pkg/services/ngalert/notifier/alertmanager_test.go
index 48efde7c517..dca2b674436 100644
--- a/pkg/services/ngalert/notifier/alertmanager_test.go
+++ b/pkg/services/ngalert/notifier/alertmanager_test.go
@@ -391,9 +391,9 @@ func TestSilenceCleanup(t *testing.T) {
 		// Active now
 		makeSilence("", "tests", dt(now.Add(-5*time.Hour)), dt(now.Add(6*time.Hour)), matchers),
 		// Expiring soon.
-		makeSilence("", "tests", dt(now.Add(-5*time.Hour)), dt(now.Add(5*time.Second)), matchers),
-		// Expiring *very* soon
 		makeSilence("", "tests", dt(now.Add(-5*time.Hour)), dt(now.Add(2*time.Second)), matchers),
+		// Expiring *very* soon
+		makeSilence("", "tests", dt(now.Add(-5*time.Hour)), dt(now.Add(1*time.Second)), matchers),
 	}
 
 	for _, s := range silences {
@@ -407,12 +407,12 @@ func TestSilenceCleanup(t *testing.T) {
 		found, err := am.ListSilences(nil)
 		require.NoError(err)
 		return len(found) == 3
-	}, 3*time.Second, 150*time.Millisecond)
+	}, 3*time.Second, 100*time.Millisecond)
 
 	// Wait again for another silence to expire.
 	require.Eventually(func() bool {
 		found, err := am.ListSilences(nil)
 		require.NoError(err)
 		return len(found) == 2
-	}, 6*time.Second, 150*time.Millisecond)
+	}, 6*time.Second, 100*time.Millisecond)
 }
diff --git a/pkg/services/ngalert/sender/router_test.go b/pkg/services/ngalert/sender/router_test.go
index ba1ee57ceef..7fd6376d8e9 100644
--- a/pkg/services/ngalert/sender/router_test.go
+++ b/pkg/services/ngalert/sender/router_test.go
@@ -31,7 +31,10 @@ import (
 	"github.com/grafana/grafana/pkg/util"
 )
 
-func TestSendingToExternalAlertmanager(t *testing.T) {
+func TestIntegrationSendingToExternalAlertmanager(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping integration test")
+	}
 	ruleKey := models.GenerateRuleKey(1)
 
 	fakeAM := NewFakeExternalAlertmanager(t)
@@ -97,7 +100,10 @@ func TestSendingToExternalAlertmanager(t *testing.T) {
 	assertAlertmanagersStatusForOrg(t, alertsRouter, ruleKey.OrgID, 0, 0)
 }
 
-func TestSendingToExternalAlertmanager_WithMultipleOrgs(t *testing.T) {
+func TestIntegrationSendingToExternalAlertmanager_WithMultipleOrgs(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping integration test")
+	}
 	ruleKey1 := models.GenerateRuleKey(1)
 	ruleKey2 := models.GenerateRuleKey(2)
 
diff --git a/pkg/services/ngalert/store/instance_database_test.go b/pkg/services/ngalert/store/instance_database_test.go
index 134ad4d4461..80b9358d682 100644
--- a/pkg/services/ngalert/store/instance_database_test.go
+++ b/pkg/services/ngalert/store/instance_database_test.go
@@ -59,9 +59,9 @@ func TestIntegrationAlertInstanceBulkWrite(t *testing.T) {
 	_, dbstore := tests.SetupTestEnv(t, baseIntervalSeconds)
 
 	orgIDs := []int64{1, 2, 3, 4, 5}
-	counts := []int{20_000, 200, 503, 0, 1256}
-	instances := []models.AlertInstance{}
-	keys := []models.AlertInstanceKey{}
+	counts := []int{10_000, 200, 503, 0, 1256}
+	instances := make([]models.AlertInstance, 0, 10_000+200+503+0+1256)
+	keys := make([]models.AlertInstanceKey, 0, 10_000+200+503+0+1256)
 
 	for i, id := range orgIDs {
 		alertRule := tests.CreateTestAlertRule(t, ctx, dbstore, 60, id)