This paper introduces empirical relations between the death rate at a given age and the remaining life expectancy at that same age. The relations prove to be of prediction accuracy exceeding that of the common alternative, extrapolation of the death rates into older ages based on data at younger ages. Being close in accuracy to models by Horiuchi, Coale and Mitra, the proposed models may be of use in cases when the latter models may not be applied because of either lack of data on old-age mortality or violation of the underlying assumptions, such as population stability. Combining the proposed models with constrained extrapolations of old-age mortality will be a useful tool in estimating and projecting old-age mortality, completing life tables for young cohorts and extending model and empirical life tables to old age.