This paper presents a fully automatic and end-to-end optimised airway segmentation method for thoracic computed tomography, based on the U-Net architecture. We use a simple and low-memory 3D U-Net as backbone, which allows the method to process large 3D image patches, often comprising full lungs, in a single pass through the network. This makes the method simple, robust and efficient. We validated the proposed method on three datasets with very different characteristics and various airway abnormalities: (1) a dataset of pediatric patients including subjects with cystic fibrosis, (2) a subset of the Danish Lung Cancer Screening Trial, including subjects with chronic obstructive pulmonary disease, and (3) the EXACT’09 public dataset. We compared our method with other state-of-the-art airway segmentation methods, including relevant learning-based methods in the literature evaluated on the EXACT’09 data. We show that our method can extract highly complete airway trees with few false positive errors, on scans from both healthy and diseased subjects, and also that the method generalizes well across different datasets. On the EXACT’09 test set, our method achieved the second highest sensitivity score among all methods that reported good specificity.