The production of β-lactamases is an effective strategy by which pathogenic bacteria can develop resistance against β-lactam antibiotics. While inhibitors of serine-β-lactamases are widely used in combination therapy with β-lactam antibiotics, there are no clinically available inhibitors of metallo-β-lactamases (MBLs), and so there is a need for the development of such inhibitors. This work describes the optimisation of a lead inhibitor previously identified by fragment screening of a compound library. We also report that thiosemicarbazide intermediates in the syntheses of these compounds are also moderately potent inhibitors of the IMP-1 MBL from Pseudomonas aeruginosa. The interactions of these inhibitors with the active site of IMP-1 were examined using in silico methods.