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Methodology is proposed of improving the extrapolations of the death rates into old age by constraining the extrapolation on presumed life expectancy. The method is particularly important in cases where the data quality at old age, in particular the age exaggeration, does not allow for drawing reliable mortality estimates. Our tests are based on period data from the Human Mortality Database and the Horiuchi-Coale and Mitra formulas for reducing the bias of life expectancy in the open age interval. We show strong improvements in the extrapolation accuracy when constraining the extrapolation on either the empirical life expectancy or the Horiuchi-Coale or Mitra estimates. Unconstrained extrapolations and those constrained by conventional life table estimates of the life expectancy show substantial biases and should be avoided. Combining extrapolation with life expectancy estimates which are robust to effects of the age exaggeration is a valuable tool for mortality estimation.