Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compact stencils and point-wise non-linearities. Commonly, the convolution operators couple features from all channels, which leads to immense computational cost in the training of and prediction with CNNs. To improve the efficiency of CNNs, we introduce lean convolution operators that reduce the number of parameters and computational complexity. Our new operators can be used in a wide range of existing CNNs. Here, we exemplify their use in residual networks (ResNets), which have been very reliable for a few years now and analyzed intensively. In our experiments on three image classification problems, the proposed LeanResNet yields results that are comparable to other recently proposed reduced architectures using similar number of parameters.