The search for druggable pockets on the surface of a protein is often performed on a single conformer, treated as a rigid body. Transient druggable pockets may be missed in this approach. Here, we describe a methodology for systematic in silico analysis of surface clefts across multiple conformers of the metastable protein α(1)-antitrypsin (A1AT). Pathological mutations disturb the conformational landscape of A1AT, triggering polymerisation that leads to emphysema and hepatic cirrhosis. Computational screens for small molecule inhibitors of polymerisation have generally focused on one major druggable site visible in all crystal structures of native A1AT. In an alternative approach, we scan all surface clefts observed in crystal structures of A1AT and in 100 computationally produced conformers, mimicking the native solution ensemble. We assess the persistence, variability and druggability of these pockets. Finally, we employ molecular docking using publicly available libraries of small molecules to explore scaffold preferences for each site. Our approach identifies a number of novel target sites for drug design. In particular one transient site shows favourable characteristics for druggability due to high enclosure and hydrophobicity. Hits against this and other druggable sites achieve docking scores corresponding to a K(d) in the µM-nM range, comparing favourably with a recently identified promising lead. Preliminary ThermoFluor studies support the docking predictions. In conclusion, our strategy shows considerable promise compared with the conventional single pocket/single conformer approach to in silico screening. Our best-scoring ligands warrant further experimental investigation.