Compression is a standard procedure for making convolutional neural networks (CNNs) adhere to some specific computing resource constraints. However, searching for a compressed architecture typically involves a series of time-consuming training/validation experiments to determine a good compromise between network size and performance accuracy. To address this, we propose an image complexity-guided network compression technique for biomedical image segmentation. Given any resource constraints, our framework utilizes data complexity and network architecture to quickly estimate a compressed model which does not require network training. Specifically, we map the dataset complexity to the target network accuracy degradation caused by compression. Such mapping enables us to predict the final accuracy for different network sizes, based on the computed dataset complexity. Thus, one may choose a solution that meets both the network size and segmentation accuracy requirements. Finally, the mapping is used to determine the convolutional layer-wise multiplicative factor for generating a compressed network. We conduct experiments using 5 datasets, employing 3 commonly-used CNN architectures for biomedical image segmentation as representative networks. Our proposed framework is shown to be effective for generating compressed segmentation networks, retaining up to $\approx 95\%$ of the full-sized network segmentation accuracy, and at the same time, utilizing $\approx 32x$ fewer network trainable weights (average reduction) of the full-sized networks.