The ICRF and WHO recently published estimates of smoking-attributed deaths in almost 50 developed countries. These estimates are derived without using any available data on the prevalence of smoking or of other risk factors in the countries concerned. This paper describes and discusses the various assumptions on which the derivation depends and shows that they are unlikely to hold in practice. ICRF/WHO attempt to control for confounding by introducing a modification to the standard attributable risk formula which they admit is "crude and arbitrary" but state is "conservative." In fact, this modified formula carries no guarantee of conservatism at all and may overestimate deaths even where there is no confounding. The validity of the ICRF/WHO estimates of smoking-attributed deaths is further undermined by the lack of correlation seen in males between the smoking prevalence rates they estimate indirectly and smoking prevalence rates actually published. The ICRF/WHO estimates of smoking-attributed deaths are shown to have no scientific basis and to be unreliable.