In the field of vision-language contrastive learning, models such as CLIP capitalize on matched image-caption pairs as positive examples and leverage within-batch non-matching pairs as negatives. This approach has led to remarkable outcomes in zero-shot image classification, cross-modal retrieval, and linear evaluation tasks. We show that the zero-shot classification and retrieval capabilities of CLIP-like models can be improved significantly through the introduction of semantically composite examples during pretraining. Inspired by CutMix in vision categorization, we create semantically composite image-caption pairs by merging elements from two distinct instances in the dataset via a novel procedure. Our method fuses the captions and blends 50% of each image to form a new composite sample. This simple technique (termed CLIP-C for CLIP Compositions), devoid of any additional computational overhead or increase in model parameters, significantly improves zero-shot image classification and cross-modal retrieval. The benefits of CLIP-C are particularly pronounced in settings with relatively limited pretraining data.