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Deep Neural Networks (DNNs) have the potential for making various clinical procedures more time-efficient by automating medical image segmentation. Due to their strong, in some cases human-level, performance, they have become the standard approach in this field. The design of the best possible medical image segmentation DNNs, however, is task-specific. Neural Architecture Search (NAS), i.e., the automation of neural network design, has been shown to have the capability to outperform manually designed networks for various tasks. However, the existing NAS methods for medical image segmentation have explored a quite limited range of types of DNN architectures that can be discovered. In this work, we propose a novel NAS search space for medical image segmentation networks. This search space combines the strength of a generalised encoder-decoder structure, well known from U-Net, with network blocks that have proven to have a strong performance in image classification tasks. The search is performed by looking for the best topology of multiple cells simultaneously with the configuration of each cell within, allowing for interactions between topology and cell-level attributes. From experiments on two publicly available datasets, we find that the networks discovered by our proposed NAS method have better performance than well-known handcrafted segmentation networks, and outperform networks found with other NAS approaches that perform only topology search, and topology-level search followed by cell-level search.