Mouse models are becoming instrumental for the study of lung disease. Due to its resolution and low cost, high resolution Computed Tomography (micro-CT) is a very adequate technology to visualize the mouse lungs in-vivo. Automatic segmentation and measurement of airways in micro-CT images of the lungs can be useful as a preliminary step prior other image analysis quantification tasks, as well as for the study of pathologies that alter the airways structure. In this paper, we present an efficient segmentation and reconstruction algorithm which simultaneously segments and reconstructs the bronchial tree, while providing the length and mean radius of each airway segment. A locally adaptive intensity threshold is used to account for the low signal to noise ratio and strong artifacts present in micro-CT images. We validate our method by comparing it with manual segmentations of 10 different scans, obtaining an average true positive volume fraction of 85.52% with a false positive volume fraction of 5.04%.