Are there any effective chemical exfoliants?

I heard that chemical exfoliation is better than physical exfoliation for thin and sensitive skin, so I've been using exfoliating toners containing AHA or BHA. However, perhaps because the product I'm currently using is too mild, I can feel my skin becoming smoother when I wash it off the next morning, but the dead skin cells just flake off when I apply makeup. It means the dead skin cells weren't actually removed. So, I have no choice but to use a peeling gel about once a week. But since peeling gels are the type that require scrubbing, my skin feels rough and irritated. Are there any effective chemical exfoliating products out there? Please recommend some good ones if you know of any.