State-of-the-art deep neural network (DNN) pruning techniques, applied one-shot before training starts, evaluate sparse architectures with the help of a single criterion -- called pruning score. Pruning weights based on a solitary score works well for some architectures and pruning rates but may also fail for other ones. As a common baseline for pruning scores, we introduce the notion of a generalized synaptic score (GSS). In this work we do not concentrate on a single pruning criterion, but provide a framework for combining arbitrary GSSs to create more powerful pruning strategies. These COmbined Pruning Scores (COPS) are obtained by solving a constrained optimization problem. Optimizing for more than one score prevents the sparse network to overly specialize on an individual task, thus COntrols Pruning before training Starts. The combinatorial optimization problem given by COPS is relaxed on a linear program (LP). This LP is solved analytically and determines a solution for COPS. Furthermore, an algorithm to compute it for two scores numerically is proposed and evaluated. Solving COPS in such a way has lower complexity than the best general LP solver. In our experiments we compared pruning with COPS against state-of-the-art methods for different network architectures and image classification tasks and obtained improved results.