A method of rolling out the ends of a coiled strip in a reversing rolling mill having reels disposed on both sides thereof minimizes a length of strip at the strip ends having a non-conforming thickness. A start of the strip is introduced into the roll gap without inlet side strip tension and without rolling force at the start of each reduction pass. The rolling force is then gradually increased. The inlet side strip tension is subsequently reduced substantially to zero at the end of each reduction pass while the strip end still connected to the uncoiling reel, such that the strip end passes tension-free completely through the rolling gap and is consequently reduced in thickness. An apparatus for carrying out the method on a reversing mill includes a control system which selectively controls, via regulating and adjusting devices, the inlet and outlet strip tensions and the rolling force in a manner dependent upon respective locations of the start and end of the strip.