Covalent enzyme inhibitors constitute a highly important group of biologically active compounds, with numerous drugs available on the market. Although the discovery of inhibitors of urease, a urea hydrolyzing enzyme crucial for the survival of some human pathogens, is a field of medicinal chemistry that has grown in recent years, covalent urease inhibitors have been rarely investigated until now. Forty Michael acceptor-type compounds were screened for their inhibitory activities against bacterial urease, and several structures exhibited high potency in the nanomolar range. The correlation between chemical reactivity towards thiols and inhibitory potency indicated the most valuable compound - acetylenedicarboxylic acid, with Ki∗=42.5nM and logkGSH=-2.14. Molecular modelling studies revealed that acetylenedicarboxylic acid is the first example of highly effective mode of binding based on simultaneous bonding to a cysteine residue and interaction with nickel ions present in the active site. Activity-reactivity profiling of reversible covalent enzyme inhibitors is a general method for the identification of valuable drug candidates.