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Supervised machine learning provides state-of-the-art solutions to a wide range of computer vision problems. However, the need for copious labelled training data limits the capabilities of these algorithms in scenarios where such input is scarce or expensive. Self-supervised learning offers a way to lower the need for manually annotated data by pretraining models for a specific domain on unlabelled data. In this approach, labelled data are solely required to fine-tune models for downstream tasks. Medical image segmentation is a field where labelling data requires expert knowledge and collecting large labelled datasets is challenging; therefore, self-supervised learning algorithms promise substantial improvements in this field. Despite this, self-supervised learning algorithms are used rarely to pretrain medical image segmentation networks. In this paper, we elaborate and analyse the effectiveness of supervised and self-supervised pretraining approaches on downstream medical image segmentation, focusing on convergence and data efficiency. We find that self-supervised pretraining on natural images and target-domain-specific images leads to the fastest and most stable downstream convergence. In our experiments on the ACDC cardiac segmentation dataset, this pretraining approach achieves 4-5 times faster fine-tuning convergence compared to an ImageNet pretrained model. We also show that this approach requires less than five epochs of pretraining on domain-specific data to achieve such improvement in the downstream convergence time. Finally, we find that, in low-data scenarios, supervised ImageNet pretraining achieves the best accuracy, requiring less than 100 annotated samples to realise close to minimal error.