Monocular depth estimation is the task of obtaining a measure of distance for each pixel using a single image. It is an important problem in computer vision and is usually solved using neural networks. Though recent works in this area have shown significant improvement in accuracy, the state-of-the-art methods tend to require massive amounts of memory and time to process an image. The main purpose of this work is to improve the performance of the latest solutions with no decrease in accuracy. To this end, we introduce the Double Refinement Network architecture. The proposed method achieves state-of-the-art results on the standard benchmark RGB-D dataset NYU Depth v2, while its frames per second rate is significantly higher (up to 18 times speedup per image at batch size 1) and the RAM usage is lower.