Fragment screens have successfully identified new scaffolds in drug discovery, often with relatively high hit rates (5%) using small screening libraries (1,000-10,000 compounds). This raises two questions: would other noteworthy chemotypes be found were one to screen all commercially available fragments (>300,000), and does the success rate imply low specificity of fragments? We used molecular docking to screen large libraries of fragments against CTX-M beta-lactamase. We identified ten millimolar-range inhibitors from the 69 compounds tested. The docking poses corresponded closely to the crystallographic structures subsequently determined. Notably, these initial low-affinity hits showed little specificity between CTX-M and an unrelated beta-lactamase, AmpC, which is unusual among beta-lactamase inhibitors. This is consistent with the idea that the high hit rates among fragments correlate to a low initial specificity. As the inhibitors were progressed, both specificity and affinity rose together, yielding to our knowledge the first micromolar-range noncovalent inhibitors against a class A beta-lactamase.