Liver segmentation is a prerequisite for various hepatic interventions and is a time-consuming manual task performed by radiology experts. Recently, various computationally expensive deep learning architectures tackled this aspect without considering the resource limitations of a real-life clinical setup. In this paper, we investigated the capabilities of a lightweight model, UNeXt, in comparison with the U-Net model. Moreover, we conduct a broad analysis at the micro and macro levels of these architectures by using two training loss functions: soft dice loss and unified focal loss, and by substituting the commonly used ReLU activation function, with the novel Funnel activation function. An automatic post-processing step that increases the overall performance of the models is also proposed. Model training and evaluation were performed on a public database—LiTS. The results show that the UNeXt model (Funnel activation, soft dice loss, post-processing step) achieved a 0.9902 dice similarity coefficient on the whole CT volumes in the test set, with 15× fewer parameters in nearly 4× less inference time, compared to its counterpart, U-Net. Thus, lightweight models can become the new standard in medical segmentation, and when implemented thoroughly can alleviate the computational burden while preserving the capabilities of a parameter-heavy architecture