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Convolutional neural networks (CNNs) have achieved astonishing advances over the past decade, defining state-of-the-art in several computer vision tasks. CNNs are capable of learning robust representations of the data directly from the RGB pixels. However, most image data are usually available in compressed format, from which the JPEG is the most widely used due to transmission and storage purposes demanding a preliminary decoding process that have a high computational load and memory usage. For this reason, deep learning methods capable of learning directly from the compressed domain have been gaining attention in recent years. Those methods usually extract a frequency domain representation of the image, like DCT, by a partial decoding, and then make adaptation to typical CNNs architectures to work with them. One limitation of these current works is that, in order to accommodate the frequency domain data, the modifications made to the original model increase significantly their amount of parameters and computational complexity. On one hand, the methods have faster preprocessing, since the cost of fully decoding the images is avoided, but on the other hand, the cost of passing the images though the model is increased, mitigating the possible upside of accelerating the method. In this paper, we propose a further study of the computational cost of deep models designed for the frequency domain, evaluating the cost of decoding and passing the images through the network. We also propose handcrafted and data-driven techniques for reducing the computational complexity and the number of parameters for these models in order to keep them similar to their RGB baselines, leading to efficient models with a better trade off between computational cost and accuracy.