Well, that's a bit too general, isn't it?
Shaving against the grain on the upper lip - The Fool's Pass - Straight Razor Place Wiki deals with the OP's specific problem, but this method is in the advanced section for a reason.
Back to the original problem. While I do a regular
multiple pass anywhere else, I've abandoned the ATG pass on the upper lip for an oblique pass, i.e steeper than an
XTG, but shallower than an
ATG pass. The result is quite similar, but the chances of skin irritation are lower.
Another factor that might induce the OP's sub optimal results may be lack of
skin stretching. It is a tad difficult on the upper lip, but a technique well worth learning. Open mouth, and a U made up of index finger and thumb have helped me.