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I also have oily skin, which is good and not so good. Straight shaving shaves everything off my face including any oils, so after the shave, I need to add some moisture back into it, but I am sensitive as to what is added.
A gentle moisturizer such as facial vitamin C cream, which I do water down with a few drops before applying works well. I also use a Nevia Balm that is for sensitive skin.
Pabster
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I'm also a victim of oily skin. I have fallen in love with the alcohol free Thayers witch hazel as an AS. It's very light but moisturizes just enough. The cucumber is what I prefer but they have a decent line up.