Four different approaches for the design of axially compressed cylindrical shells are presented, namely (1) the knockdown factor (KDF) concept, (2) the single perturbation load approach, (3) a probabilistic design procedure and (4) the convex anti-optimization approach. The different design approaches take the imperfection sensitivity and the scatter of input parameters into account differently. In this paper, the design of a composite cylinder is optimized considering the ply angles as design variables. The KDF concept provides a very conservative design load and in addition an imperfection sensitive design, whereas the other approaches lead to a significantly less conservative design load and to a less imperfection sensitive design configuration. The ways in which imperfection sensitivity is treated by the different approaches and how these influence the optimal design configuration is discussed.