Abstract: Neural video compression has emerged as a novel paradigm combining trainable multilayer neural net-works and machine learning, achieving competitive rate-distortion (RD) performances, but still remaining impractical due to heavy neural architectures, with large memory and computational demands. In addition, models are usually optimized for a single RD tradeoff. Recent slimmable image codecs can dynamically adjust their model capacity to gracefully reduce the memory and computation requirements, without harming RD performance. In this paper we propose a slimmable video codec (SlimVC), by integrating a slimmable temporal entropy model in a slimmable autoencoder. Despite a significantly more complex architecture, we show that slimming remains a powerful mechanism to control rate, memory footprint, computational cost and latency, all being important requirements for practical video compression.