As massively parallel computations have become broadly available with modern GPUs, deep architectures trained on very large datasets have risen in popularity. Discriminatively trained convolutional neural networks, in particular, were recently shown to yield state-of-the-art performance in challenging image classification benchmarks such as ImageNet. However, elements of these architectures are similar to standard hand-crafted representations used in computer vision. In this paper, we explore the extent of this analogy, proposing a version of the state-of-the-art Fisher vector image encoding that can be stacked in multiple layers. This architecture significantly improves on standard Fisher vectors, and obtains competitive results with deep convolutional networks at a significantly smaller computational cost. Our hybrid architecture allows us to measure the performance improvement brought by a deeper image classification pipeline, while staying in the realms of conventional SIFT features and FV encodings.