In this paper, we propose different strategies for simplifying filters, used as feature extractors, to be learnt in convolutional neural networks (ConvNets) in order to modify the hypothesis space, and to speed-up learning and processing times. We study two kinds of filters that are known to be computationally efficient in feed-forward processing: fused convolution/sub-sampling filters, and separable filters. We compare the complexity of the back-propagation algorithm on ConvNets based on these different kinds of filters. We show that using these filters allows to reach the same level of recognition performance as with classical ConvNets for handwritten digit recognition, up to 3.3 times faster.