A new pansharpening method is proposed, based on convolutional neural networks. We adapt a simple and effective three-layer architecture recently proposed for super-resolution to the pansharpening problem. Moreover, to improve performance without increasing complexity, we augment the input by including several maps of nonlinear radiometric indices typical of remote sensing. Experiments on three representative datasets show the proposed method to provide very promising results, largely competitive with the current state of the art in terms of both full-reference and no-reference metrics, and also at a visual inspection.