diff --git a/client_test.go b/client_test.go
index 481db6d..c240a1f 100644
--- a/client_test.go
+++ b/client_test.go
@@ -417,6 +417,67 @@ func TestClient_DialWithContext(t *testing.T) {
 	}
 }
 
+// TestClient_DialWithContextInvalidHost tests the DialWithContext method with intentional breaking
+// for the Client object
+func TestClient_DialWithContextInvalidHost(t *testing.T) {
+	c, err := getTestConnection(true)
+	if err != nil {
+		t.Skipf("failed to create test client: %s. Skipping tests", err)
+	}
+	c.co = nil
+	c.host = "invalid.addr"
+	ctx := context.Background()
+	if err := c.DialWithContext(ctx); err == nil {
+		t.Errorf("dial succeeded but was supposed to fail")
+		return
+	}
+}
+
+// TestClient_DialWithContextInvalidHELO tests the DialWithContext method with intentional breaking
+// for the Client object
+func TestClient_DialWithContextInvalidHELO(t *testing.T) {
+	c, err := getTestConnection(true)
+	if err != nil {
+		t.Skipf("failed to create test client: %s. Skipping tests", err)
+	}
+	c.co = nil
+	c.helo = ""
+	ctx := context.Background()
+	if err := c.DialWithContext(ctx); err == nil {
+		t.Errorf("dial succeeded but was supposed to fail")
+		return
+	}
+}
+
+// TestClient_DialWithContextInvalidAuth tests the DialWithContext method with intentional breaking
+// for the Client object
+func TestClient_DialWithContextInvalidAuth(t *testing.T) {
+	c, err := getTestConnection(true)
+	if err != nil {
+		t.Skipf("failed to create test client: %s. Skipping tests", err)
+	}
+	c.user = "invalid"
+	c.pass = "invalid"
+	c.SetSMTPAuthCustom(auth.LoginAuth("invalid", "invalid", "invalid"))
+	ctx := context.Background()
+	if err := c.DialWithContext(ctx); err == nil {
+		t.Errorf("dial succeeded but was supposed to fail")
+		return
+	}
+}
+
+// TestClient_checkConn tests the checkConn method with intentional breaking for the Client object
+func TestClient_checkConn(t *testing.T) {
+	c, err := getTestConnection(true)
+	if err != nil {
+		t.Skipf("failed to create test client: %s. Skipping tests", err)
+	}
+	c.co = nil
+	if err := c.checkConn(); err == nil {
+		t.Errorf("connCheck() should fail but succeeded")
+	}
+}
+
 // TestClient_DiealWithContextOptions tests the DialWithContext method plus different options
 // for the Client object
 func TestClient_DialWithContextOptions(t *testing.T) {
@@ -468,6 +529,9 @@ func TestClient_DialWithContextOptions(t *testing.T) {
 // getTestConnection takes environment variables to establish a connection to a real
 // SMTP server to test all functionality that requires a connection
 func getTestConnection(auth bool) (*Client, error) {
+	if os.Getenv("TEST_SKIP_ONLINE") != "" {
+		return nil, fmt.Errorf("env variable TEST_SKIP_ONLINE is set. Skipping online tests")
+	}
 	th := os.Getenv("TEST_HOST")
 	if th == "" {
 		return nil, fmt.Errorf("no TEST_HOST set")
diff --git a/header_test.go b/header_test.go
new file mode 100644
index 0000000..59a627d
--- /dev/null
+++ b/header_test.go
@@ -0,0 +1,39 @@
+package mail
+
+import (
+	"testing"
+)
+
+// TestImportance_StringFuncs tests the different string method of the Importance object
+func TestImportance_StringFuncs(t *testing.T) {
+	tests := []struct {
+		name   string
+		imp    Importance
+		wantns string
+		xprio  string
+		want   string
+	}{
+		{"Importance: Non-Urgent", ImportanceNonUrgent, "0", "5", "non-urgent"},
+		{"Importance: Low", ImportanceLow, "0", "5", "low"},
+		{"Importance: Normal", ImportanceNormal, "", "", ""},
+		{"Importance: High", ImportanceHigh, "1", "1", "high"},
+		{"Importance: Urgent", ImportanceUrgent, "1", "1", "urgent"},
+		{"Importance: Unknown", 9, "", "", ""},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if tt.imp.NumString() != tt.wantns {
+				t.Errorf("wrong number string for Importance returned. Expected: %s, got: %s",
+					tt.wantns, tt.imp.NumString())
+			}
+			if tt.imp.XPrioString() != tt.xprio {
+				t.Errorf("wrong x-prio string for Importance returned. Expected: %s, got: %s",
+					tt.xprio, tt.imp.XPrioString())
+			}
+			if tt.imp.String() != tt.want {
+				t.Errorf("wrong string for Importance returned. Expected: %s, got: %s",
+					tt.want, tt.imp.String())
+			}
+		})
+	}
+}