The existing experimental data for the half-lives of the uranium isotopes 238U and 235U have been scrutinised in detail because of their significant practical importance, in particular for geochronogical use and for the assay of standard samples used for neutron fluence and cross-section measurements. The most accurate measurements by Jaffey et al. (Phys. Rev. C 4 (5) 1889) with 1sigma uncertainties of 0.054% (238U) and 0.068% (235U), are not confirmed by other measurements of comparable accuracy. In this work, we take a critical look at the 238U and 235U half-life measurements in the literature. Although we find that the Jaffey et al. data are concordant with other reliable results, generally much higher uncertainties of the latter cannot prove or disprove the Jaffey et al. results. Therefore, at this time, we do not recommend new half-life values. Instead, we call for new measurements of these two half-lives with accuracies comparable to the work of Jaffey et al.