Optic disc segmentation is a crucial step in the development of automated tools for the detection and diagnosis of optical pathologies such as glaucoma. In this paper, we build upon our previous work, where we introduced the Fine-Net  - a Convolutional Neural Network (CNN) for optic disc segmentation. In this work, we introduce a prior CNN called the P-Net, which is arranged in cascade with the Fine-Net, to generate a more accurate optic disc segmentation map. The P-Net generates a low-resolution (256 × 256) segmentation map which is then further upscaled along with the input image and is fed to the Fine-Net, which yields a high-resolution segmentation map (1024 × 1024). Both CNNs are separately trained on publicly available datasets: DRISHTI-GS, MESSIDOR, and DRIONS-DB. We demonstrate the advantage of providing a prior segmentation map via the P-Net and further improve on our previous predictions. We obtain state-of-the-art results with an average Dice coefficient of 0.966 and Jaccard coefficient of 0.934.