Tips for laning against Gnarr

I'm having some trouble in matchups against Gnarr. I've tried lulu, and Vlad vs him however on Lulu, i find gnarr has very short cooldowns for being resourceless, can push the wave almost as fast as i can and doesn't have to contend with mana. I've played a number of Lulu vs Gnarr, and tried slow pushing him in, and fast pushing, both without favorable results. attempting to freeze just gets me pushed in.

While I can eventually push him in, i usually go OOM by the time i hit his tower (level 5-6), and I'm way too open to his mega Gnarr form and ganks. Tried going resourcless / sustain with Vlad, but gnar can push faster until I get a few points in e, and does waaaay more damage than Vlad can (then again, who doesn't? =p).

I was wondering if anyone had any tips or counterpicks for playing against Gnarr in the top lane. His bully presence is a little much, and i'd like to start taking care of the little runt.