I don't think the CV bars have mineral oil in them, but they do have castor oil. That can be problematic for some people, but not all.
Grand Goobah Caedran, Aqueous Infusion of Demulcents, Order of the Curly Crusaders

Fia 2cFi, fine texture, med porosity CG 5-29-09 * My hair loves protein! Currently using : DermOrganics Shampoo and IHM, G2B Kinkier Mousse, Re:Coil VMM, Anything Spiral Solutions! MO Sealing. Coconut Oil Pre-Poo, once a month Hard Water shampoo. Avoiding Glycerin in finishing products.