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The computation and memory needed for Convolutional Neural Network (CNN) inference can be reduced by pruning weights from the trained network. Pruning is guided by a pruning saliency, which heuristically approximates the change in the loss function associated with the removal of specific weights. Many pruning signals have been proposed, but the performance of each heuristic depends on the particular trained network. This leaves the data scientist with a difficult choice. When using any one saliency metric for the entire pruning process, we run the risk of the metric assumptions being invalidated, leading to poor decisions being made by the metric. Ideally we could combine the best aspects of different saliency metrics. However, despite an extensive literature review, we are unable to find any prior work on composing different saliency metrics. The chief difficulty lies in combining the numerical output of different saliency metrics, which are not directly comparable. We propose a method to compose several primitive pruning saliencies, to exploit the cases where each saliency measure does well. Our experiments show that the composition of saliencies avoids many poor pruning choices identified by individual saliencies. In most cases our method finds better selections than even the best individual pruning saliency.