The water in my kitchen sink takes about 2-4 seconds to completely stop running after I turn the water off. My faucet has two handles - one for hot and one for cold water. We thought the old faucet may have been the problem so we replaced it with a new one yesterday. The problem is still there.

A couple of years ago we experienced the same problem. I shut the water valves off under the sink after learning that we have air in the lines. We turned the handles to the on position then turned the valves back on. The water sputtered at first, I suppose the air was escaping, and the problem was solved. This trick is not working now. Any suggestions?

Remove the aerator and see what happens.

More than likely its all to do with atmospheric pressure in the spout of the tap that is causing the water to dribble after turning it off, had this problem the other day and I did fix it by changing the cartridges in the handles. You may need the spout tightened up as well to stop letting the air flow through the tap.