So neither my girlfriend nor I am all that experienced prior to getting together. But we have been having sex and having some issues with the condom slipping off.

I think this might be due to the fact that my penis is thicker at the base and thinner at the tip (somewhat cone-shaped, like not absurdly so). And it feels like when we have sex the condom gradually starts to slip down my penis and then sometimes slips off entirely. This is even though the condom feels pretty tight around the base of my dick. It's that once it starts riding up then it is looser further up. I think this is due to the shape of my penis.

We have been using Trojan Ultra Thins primarily and they generally feel pretty good to me. But I'm wondering if there might be something better based on the shape of my penis. Obviously I don't want to get her pregnant accidentally and this is becoming a frustrating issue for both of us. We can't switch to an IUD right now for unrelated reasons.