diff --git a/map_claims_test.go b/map_claims_test.go
index 5c3a5c18..b4af574b 100644
--- a/map_claims_test.go
+++ b/map_claims_test.go
@@ -134,3 +134,56 @@ func TestMapClaimsVerifyExpiresAtExpire(t *testing.T) {
 		t.Fatalf("Failed to verify claims, wanted: %v got %v", want, (got == nil))
 	}
 }
+
+func TestMapClaims_ParseString(t *testing.T) {
+	type args struct {
+		key string
+	}
+	tests := []struct {
+		name    string
+		m       MapClaims
+		args    args
+		want    string
+		wantErr bool
+	}{
+		{
+			name: "missing key",
+			m:    MapClaims{},
+			args: args{
+				key: "mykey",
+			},
+			want:    "",
+			wantErr: false,
+		},
+		{
+			name: "wrong key type",
+			m:    MapClaims{"mykey": 4},
+			args: args{
+				key: "mykey",
+			},
+			want:    "",
+			wantErr: true,
+		},
+		{
+			name: "correct key type",
+			m:    MapClaims{"mykey": "mystring"},
+			args: args{
+				key: "mykey",
+			},
+			want:    "mystring",
+			wantErr: false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got, err := tt.m.ParseString(tt.args.key)
+			if (err != nil) != tt.wantErr {
+				t.Errorf("MapClaims.ParseString() error = %v, wantErr %v", err, tt.wantErr)
+				return
+			}
+			if got != tt.want {
+				t.Errorf("MapClaims.ParseString() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
diff --git a/parser_test.go b/parser_test.go
index 5cf84e08..306f8b50 100644
--- a/parser_test.go
+++ b/parser_test.go
@@ -56,6 +56,28 @@ var jwtTestData = []struct {
 	parser        *jwt.Parser
 	signingMethod jwt.SigningMethod // The method to sign the JWT token for test purpose
 }{
+	{
+		"invalid JWT",
+		"thisisnotreallyajwt",
+		defaultKeyFunc,
+		nil,
+		false,
+		jwt.ValidationErrorMalformed,
+		[]error{jwt.ErrTokenMalformed},
+		nil,
+		jwt.SigningMethodRS256,
+	},
+	{
+		"bearer in JWT",
+		"bearer eyJ0eXAiOiJKV1QiLCJhbGciOiJSUzI1NiJ9.eyJmb28iOiJiYXIifQ.FhkiHkoESI_cG3NPigFrxEk9Z60_oXrOT2vGm9Pn6RDgYNovYORQmmA0zs1AoAOf09ly2Nx2YAg6ABqAYga1AcMFkJljwxTT5fYphTuqpWdy4BELeSYJx5Ty2gmr8e7RonuUztrdD5WfPqLKMm1Ozp_T6zALpRmwTIW0QPnaBXaQD90FplAg46Iy1UlDKr-Eupy0i5SLch5Q-p2ZpaL_5fnTIUDlxC3pWhJTyx_71qDI-mAA_5lE_VdroOeflG56sSmDxopPEG3bFlSu1eowyBfxtu0_CuVd-M42RU75Zc4Gsj6uV77MBtbMrf4_7M_NUTSgoIF3fRqxrj0NzihIBg",
+		defaultKeyFunc,
+		nil,
+		false,
+		jwt.ValidationErrorMalformed,
+		[]error{jwt.ErrTokenMalformed},
+		nil,
+		jwt.SigningMethodRS256,
+	},
 	{
 		"basic",
 		"eyJ0eXAiOiJKV1QiLCJhbGciOiJSUzI1NiJ9.eyJmb28iOiJiYXIifQ.FhkiHkoESI_cG3NPigFrxEk9Z60_oXrOT2vGm9Pn6RDgYNovYORQmmA0zs1AoAOf09ly2Nx2YAg6ABqAYga1AcMFkJljwxTT5fYphTuqpWdy4BELeSYJx5Ty2gmr8e7RonuUztrdD5WfPqLKMm1Ozp_T6zALpRmwTIW0QPnaBXaQD90FplAg46Iy1UlDKr-Eupy0i5SLch5Q-p2ZpaL_5fnTIUDlxC3pWhJTyx_71qDI-mAA_5lE_VdroOeflG56sSmDxopPEG3bFlSu1eowyBfxtu0_CuVd-M42RU75Zc4Gsj6uV77MBtbMrf4_7M_NUTSgoIF3fRqxrj0NzihIBg",
@@ -371,10 +393,12 @@ func TestParser_Parse(t *testing.T) {
 				token, err = parser.ParseWithClaims(data.tokenString, jwt.MapClaims{}, data.keyfunc)
 			case *jwt.RegisteredClaims:
 				token, err = parser.ParseWithClaims(data.tokenString, &jwt.RegisteredClaims{}, data.keyfunc)
+			case nil:
+				token, err = parser.ParseWithClaims(data.tokenString, nil, data.keyfunc)
 			}
 
 			// Verify result matches expectation
-			if !reflect.DeepEqual(data.claims, token.Claims) {
+			if data.claims != nil && !reflect.DeepEqual(data.claims, token.Claims) {
 				t.Errorf("[%v] Claims mismatch. Expecting: %v  Got: %v", data.name, data.claims, token.Claims)
 			}
 
@@ -386,7 +410,10 @@ func TestParser_Parse(t *testing.T) {
 				t.Errorf("[%v] Invalid token passed validation", data.name)
 			}
 
-			if (err == nil && !token.Valid) || (err != nil && token.Valid) {
+			// Since the returned token is nil in the ErrTokenMalformed, we
+			// cannot make the comparison here
+			if !errors.Is(err, jwt.ErrTokenMalformed) &&
+				((err == nil && !token.Valid) || (err != nil && token.Valid)) {
 				t.Errorf("[%v] Inconsistent behavior between returned error and token.Valid", data.name)
 			}