Abstract: A method of reducing the thickness of a slab of metal under conditions that tend to produce alligator defects in the ends of the slab, the method comprising the steps of tapering at least one end of the slab and directing the same into a rolling mill. The tapered end of the slab is reduced in thickness in the mill, the amount of reduction increasing as the tapered end passes through the mill. The slab continues through the mill to reduce the thickness of the same. The end of the slab is again tapered and directed again through a rolling mill, with each of said tapers providing combinations of entry thickness to thickness reduction such that the reduction taken in the area of each taper is in an entry thickness to thickness reduction zone that does not produce alligatoring in the ends of the slab. The remaining untapered portion of the slab is reduced in thickness in the mill in an entry thickness to thickness reduction zone in which alligator formation tends to occur.