Deep facial cleansing creams may sound too comprehensive for a daily use like makeup removal, but when formulated for oily skin, they can provide excellent results by not only ridding your skin of layers of powder and cover-up, but also clearing out blocked pores. However, because of their strength, these types of cleansers are best suited for once-a-day use -- in this case, at the end of the day to clear off your makeup.
Many deep cleansing products take the user's skin pH level into account, and sometimes come in a slightly more acidic form because it helps to break up sebum. Oily skin can handle this better than dry and sensitive skin types, but you'll still want to shy away from cleansers with too high of a pH level, because it can dry out your skin too much.
For a daily cleanser, you'll also want to avoid alpha hydroxy acids (AHAs), salicylic acid and alcohol in the ingredients listing. While these can be useful in cleansing and dealing with acne on an occasional basis, they tend to be too harsh for daily makeup removal. They also tend to dry out your skin, which can lead your body to make more sebum.
Even with oily skin, harsh cleaners can cause more damage than good, a fact we'll look at in the next section.