Hyperspectral imaging provides a useful tool for extracting complex information when visual spectral bands are not enough to solve certain tasks. However, processing hyperspectral images (HSIs) is usually computationally expensive due to the great amount of both spatial and spectral data they incorporate. We present a low-cost convolutional neural network designed for HSI classification. Its architecture consists of two parts: a series of densely connected three-dimensional (3-D) convolutions used as a feature extractor, and a series of two-dimensional (2-D) separable convolutions used as a spatial encoder. We show that this design involves fewer trainable parameters compared to other approaches, yet without detriment to its performance. What is more, we achieve comparable state-of-the-art results testing our architecture on four public remote sensing datasets: Indian Pines, Pavia University, Salinas, and EuroSAT; and a dataset of Kochia leaves [Bassia scoparia] with three different levels of herbicide resistance. The source code and datasets are available online. (Hyper3DNet codebase: https://github.com/GiorgioMorales/hyper3dnet.)