Segmenting images of the human eye is a critical step in several tasks like iris recognition, eye tracking or pupil tracking. There are a lot of well-established hand-crafted methods that have been used in commercial practice. However, with the advances in deep learning, several deep network approaches outperform the handcrafted methods. Many of the approaches adapt the U-Net architecture for the segmentation task. In this paper we propose some simple and effective new modifications of U-Net, e.g. the increase in size of convolutional kernels, which can improve the segmentation results compared to the original U-Net design. Using these modifications, we show that we can reach state-of-the-art performance using less model parameters. We describe our motivation for the changes in the architecture, inspired mostly by the hand-crafted methods and basic image processing principles and finally we show that our optimized model slightly outperforms the original U-Net and the other state-of-the-art models.