The primary objective in cutting and packing problems is trim loss or material input minimization (in stock cutting) or value maximization (in knapsack-type problems). However, in real-life production we usually have many other objectives (costs) and constraints. Probably the most complex auxiliary criteria in one- dimensional stock cutting are the number of different cutting patterns (setups) and the maximum number of open stacks during the cutting process. There are applications where the number of stacks is restricted to two. We design a sequential heuristic to minimize material input and show its high effectiveness for this purpose. Then we extend it to restrict the number of open stacks to any given limit. Then, the heuristic is simplified and integrated into a setup-minimization approach in order to combine setup and open-stacks minimization. To get a smaller number of open stacks, we may split up the problem into several parts of smaller sizes. Different solutions are evaluated in relation to the multiple objectives using the Pareto criterion.