Abstract. We consider two- and three-dimensional bin packing problems where 90◦ rotations are allowed. We improve all known asymptotic performance bounds for these problems. In particular, we show how to combine ideas from strip packing and two-dimensional bin packing to give a new algorithm for the three-dimensional strip packing problem where boxes can only be rotated sideways. We propose to call this problem ‘This side up’. Our algorithm has an asymptotic performance bound of 9/4.