I use the Sally Hansen warm wax that comes in a jar with its own warmer. I know it sounds harsh, but it's very gentle if used correctly. I heat the wax just until it's creamy (not clear--that's too hot). Spread it on with the popsicle-type stick they give you, wait just a few seconds until you can press it, and remove fast while holding your skin with the other hand.
No redness, no irritation, and a much closer job than a razor. I do the area under my lower lip too. No one can see the hair, but I can feel it when I run my upper lip over it, I love when it feels smooth! Harsh sounding, I know, but if you hold your skin with your other hand (very important) it's just as gentle as shaving and lasts longer.