Unity 3D Rotate towards target around one local axis

using UnityEngine;
using System.Collections;

public class Turret : MonoBehaviour {

    public Transform target;
    public float rotateSpeed = 45;

    // Update is called once per frame
    void Update () {

        var localTarget = transform.InverseTransformPoint(target.position);
        localTarget.y = 0;
        var targetRot = transform.rotation * Quaternion.LookRotation( localTarget );
        transform.rotation = Quaternion.RotateTowards( transform.rotation, targetRot, Time.deltaTime * rotateSpeed );

    }
}