Cleland and Kreevoy recently advanced the idea that a special type of hydrogen bond (H-bond), termed a low-barrier hydrogen bond (LBHB), may account for the "missing" transition state stabilization underlying the catalytic power of many enzymes, and Frey et al. have proposed that the H-bond between aspartic acid 102 and histidine 57 in the catalytic triad of serine proteases is an example of a catalytically important LBHB. Experimental facts are here considered regarding the aspartic acid-histidine and cis-urocanic H-bonds that are inconsistent with fundamental tenets of the LBHB hypothesis. The inconsistencies between theory and experiment in these paradigm systems cast doubt on the existence of LBHBs, as currently defined, within enzyme active sites.