Recent years have seen a surge of interest in deep neural networks fueled by their successful applications in numerous image processing and computer vision tasks. However, such applications typically come with huge computational loads. In this article, we explore the possibility of using small neural networks to denoise images. In particular, we present SSaNN (Self-Similarity and Neural Networks), a denoising algorithm which combines the strength of BM3D on large-scale structured patterns with that of neural networks on small-scale texture content. This algorithm is able to produce a better overall recovery than both BM3D and small neural networks.