This works explores the benefits of structured parameter pruning in the framework of the MPEG standardization efforts for neural network compression. First less relevant parameters are pruned from the network, then remaining parameters are quantized and finally quantized parameters are entropy coded. We consider an unstructured pruning strategy that maximizes the number of pruned parameters at the price of randomly sparse tensors and a structured strategy that prunes fewer parameters yet yields regularly sparse tensors. We show that structured pruning enables better end-to-end compression despite lower pruning ratio because it boosts the efficiency of the arithmetic coder. As a bonus, once decompressed, the network memory footprint is lower as well as its inference time.