Deep learning models are widely used to process Computed Tomography (CT) data in the automated screening of pulmonary diseases, significantly reducing the workload of physicians. However, the three-dimensional nature of CT volumes involves an excessive number of voxels, which significantly increases the complexity of model processing. Previous screening approaches often overlook this issue, which undoubtedly reduces screening efficiency. Towards efficient and effective screening, we design a hierarchical approach to reduce the computational cost of pulmonary disease screening. The new approach re-organizes the screening workflows into three steps. First, we propose a Computed Tomography Volume Compression (CTVC) method to select a small slice subset that comprehensively represents the whole CT volume. Second, the selected CT slices are used to detect pulmonary diseases coarsely via a lightweight classification model. Third, an uncertainty measurement strategy is applied to identify samples with low diagnostic confidence, which are re-detected by radiologists. Experiments on two public pulmonary disease datasets demonstrate that our approach achieves comparable accuracy and recall while reducing the time by 50%-70% compared with the counterparts using full CT volumes. Besides, we also found that our approach outperforms previous cutting-edge CTVC methods in retaining important indications after compression.