diff --git a/storage/conformance/conformance.go b/storage/conformance/conformance.go
index 92a48d6a..8a55a75b 100644
--- a/storage/conformance/conformance.go
+++ b/storage/conformance/conformance.go
@@ -160,6 +160,9 @@ func testAuthRequestCRUD(t *testing.T, s storage.Storage) {
 	if err := s.DeleteAuthRequest(a2.ID); err != nil {
 		t.Fatalf("failed to delete auth request: %v", err)
 	}
+
+	_, err = s.GetAuthRequest(a1.ID)
+	mustBeErrNotFound(t, "auth request", err)
 }
 
 func testAuthCodeCRUD(t *testing.T, s storage.Storage) {
@@ -213,7 +216,7 @@ func testAuthCodeCRUD(t *testing.T, s storage.Storage) {
 
 	got, err := s.GetAuthCode(a1.ID)
 	if err != nil {
-		t.Fatalf("failed to get auth req: %v", err)
+		t.Fatalf("failed to get auth code: %v", err)
 	}
 	if a1.Expiry.Unix() != got.Expiry.Unix() {
 		t.Errorf("auth code expiry did not match want=%s vs got=%s", a1.Expiry, got.Expiry)
@@ -812,7 +815,7 @@ func testGC(t *testing.T, s storage.Storage) {
 			}
 		}
 		if _, err := s.GetAuthRequest(a.ID); err != nil {
-			t.Errorf("expected to be able to get auth code after GC: %v", err)
+			t.Errorf("expected to be able to get auth request after GC: %v", err)
 		}
 	}
 
@@ -823,7 +826,7 @@ func testGC(t *testing.T, s storage.Storage) {
 	}
 
 	if _, err := s.GetAuthRequest(a.ID); err == nil {
-		t.Errorf("expected auth code to be GC'd")
+		t.Errorf("expected auth request to be GC'd")
 	} else if err != storage.ErrNotFound {
 		t.Errorf("expected storage.ErrNotFound, got %v", err)
 	}
diff --git a/storage/conformance/transactions.go b/storage/conformance/transactions.go
index dc1be1b6..2fc6755b 100644
--- a/storage/conformance/transactions.go
+++ b/storage/conformance/transactions.go
@@ -135,8 +135,8 @@ func testKeysConcurrentUpdate(t *testing.T, s storage.Storage) {
 	for i := 0; i < 2; i++ {
 		n := time.Now().UTC().Round(time.Second)
 		keys1 := storage.Keys{
-			SigningKey:    jsonWebKeys[0].Private,
-			SigningKeyPub: jsonWebKeys[0].Public,
+			SigningKey:    jsonWebKeys[i].Private,
+			SigningKeyPub: jsonWebKeys[i].Public,
 			NextRotation:  n,
 		}