How can I fix a tap that still drips after I have replaced washer?

I have twice replaced the washer in the bathroom cold tap and initially it's fine. Then after a week or so, it starts to drip again, not only drip but a contant trickle. There seems to be a certain point where it doesn't drip, but if you turn the tap off all the way it drips and you have to go back the other way a little to get it to stop or at least slow the dripping. I used some supposedly super new style washer with a reservoir shaped bit of rubber, I don't really understand what's meant to be so much better about them. I've put 2 new ones on and have the same problem?