We examine the data and techniques underlying the estimation of mortality rates at older ages in Ireland since 1950. Previous attempts to elucidate the level and trends in mortality at advanced ages in Ireland have been frustrated by significant non-random biases arising from age exaggeration and age heaping, together with a lack of correspondence, growing with increasing age, between the exposed-to-risk estimated from census data and the death count from registration data. Applying the method of extinct generations, we re-estimate crude mortality rates and report the somewhat unexpected result that mortality rates were lower, and did not increase as steeply with age, than those recorded in the official Irish Life Tables. The reestimated crude rates show, for both sexes, a very slight decrease in mortality rates between the 1950s and 1980s up to age 90 years, with no improvement discernible at older ages. Improvements at advanced ages in Ireland have lagged behind those in England and Wales and other developed countries over the same period. The companion paper, Mortality in Ireland at Advanced Ages, 1950–2006: Part 2: Graduated Rates, Whelan (2009), graduates the crude rates and extends the method of extinct generations to estimate mortality rates of more recent, still surviving, generations.