Recent progress in encoder-decoder neural network architecture design has led to significant performance improvements in a wide range of medical image segmentation tasks. However, state-of-the-art networks for a given task may be too computationally demanding to run on affordable hardware, and thus users often resort to practical workarounds by modifying various macro-level design aspects. Two common examples are downsampling of the input images and reducing the network depth or size to meet computer memory constraints. In this paper, we investigate the effects of these changes on segmentation performance and show that image complexity can be used as a guideline in choosing what is best for a given dataset. We consider four statistical measures to quantify image complexity and evaluate their suitability on ten different public datasets. For the purpose of our illustrative experiments, we use DeepLabV3+ (deep large-size), M2U-Net (deep lightweight), U-Net (shallow large-size), and U-Net Lite (shallow lightweight). Our results suggest that median frequency is the best complexity measure when deciding on an acceptable input down-sampling factor and using a deep versus shallow, large-size versus lightweight network. For high-complexity datasets, a lightweight network running on the original images may yield better segmentation results than a large-size network running on downsampled images, whereas the opposite may be the case for low-complexity images.