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We address the challenge of getting efficient yet accurate recognition systems with limited labels. While recognition models improve with model size and amount of data, many specialized applications of computer vision have severe resource constraints both during training and inference. Transfer learning is an effective solution for training with few labels, however often at the expense of a compu- tationally costly fine-tuning of large base models. We propose to mitigate this unpleasant trade-off between compute and accuracy via semi-supervised cross- domain distillation from a set of diverse source models. Initially, we show how to use task similarity metrics to select a single suitable source model to distill from, and that a good selection process is imperative for good downstream performance of a target model. We dub this approach DISTILLNEAREST. Though effective, DISTILLNEAREST assumes a single source model matches the target task, which is not always the case. To alleviate this, we propose a weighted multi-source distilla- tion method to distill multiple source models trained on different domains weighted by their relevance for the target task into a single efficient model (named DISTILL- WEIGHTED). Our methods need no access to source data, and merely need features and pseudo-labels of the source models. When the goal is accurate recognition under computational constraints, both DISTILLNEAREST and DISTILLWEIGHTED approaches outperform both transfer learning from strong ImageNet initializations as well as state-of-the-art semi-supervised techniques such as FixMatch. Averaged over 8 diverse target tasks our multi-source method outperforms the baselines by 5.6%-points and 4.5%-points, respectively.