The paper aims at improving the accuracy of the extrapolations of the death rates into old age by constraining the extrapolation model on presumed life expectancy at old age. Such a task 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 (HMD 2016). We show strong improvements in the extrapolation accuracy when constraining the extrapolation on either the empirical life expectancy or the Horiuchi-Coale (1982) or Mitra (1984) estimates. Unconstrained extrapolations and those constrained by conventional life table estimates of the life expectancy in the open age interval show substantial biases and should be avoided. Combining extrapolation with life expectancy estimates which are robust to effects of the age exaggeration appear to be a valuable tool for mortality estimation.