Utilizing massive web-scale datasets has led to unprecedented performance gains in machine learning models, but also imposes outlandish compute requirements for their training. In order to improve training and data efficiency, we here push the limits of pruning large-scale multimodal datasets for training CLIP-style models. Today’s most effective pruning method on ImageNet clusters data samples into separate concepts according to their embedding and prunes away the most proto- typical samples. We scale this approach to LAION and improve it by noting that the pruning rate should be concept-specific and adapted to the complexity of the concept. Using a simple and intuitive complexity measure, we are able to reduce the training cost to a quarter of regular training. More specifically, we are able to outperform the LAION-trained OpenCLIP-ViT-B/32 model on ImageNet zero-shot accuracy by 1.1p.p. while only using 27.7% of the data and training compute. On the DataComp Medium benchmark, we achieve a new state-of-the-art ImageNet zero-shot accuracy and a competitive average zero-shot accuracy on 38 evaluation tasks.