i also recommend the tea tree oil/steam process-but it needn't be done daily.
in between, you can do 'olive oil wash.' spread a bit of olive oil over your face; let sit for a couple of minutes, and then wipe away with a soft face cloth. it removes dirt, opens pores, draws out yuck, and moisturizes (which is often why we break out). so, it's a great alternative.
it's not vegan, but also excellent, is honey--particularly if one has cystic acne (big cyst-like pimples). it's antibiotic properties kill the bacteria. you use the same process as olive oil, follwed by a water rinse.