Convolutional neural networks (CNNs) provide the current state of the art in visual object classification, but they are far less accurate when classifying partially occluded objects. A straightforward way to improve classification under occlusion conditions is to train the classifier using partially occluded object examples. However, training the network on many combinations of object instances and occlusions may be computationally expensive. This work proposes an alternative approach to increasing the robustness of CNNs to occlusion. We start by studying the effect of partial occlusions on the trained CNN and show, empirically, that training on partially occluded examples reduces the spatial support of the filters. Building upon this finding, we argue that smaller filter support is beneficial for occlusion robustness. We propose a training process that uses a special regularization term that acts to shrink the spatial support of the filters. We consider three possible regularization terms that are based on second central moments, group sparsity, and mutually reweighted L1, respectively. When trained on normal (unoccluded) examples, the resulting classifier is highly robust to occlusions. For large training sets and limited training time, the proposed classifier is even more accurate than standard classifiers trained on occluded object examples.