The rate of mortality increase with age tends to slow down at very old ages. One explanation proposed for this deceleration is the selective survival of healthier individuals to older ages. Data on mortality in Sweden and Japan are generally compatible with three predictions of this hypothesis: (1) decelerations for most major causes of death; (2) decelerations starting at younger ages for more "selective" causes; and (3) a shift of the deceleration to older ages with declining levels of mortality. A parametric model employed to illustrate the third prediction relies on the distinction between senescent and background mortality. This dichotomy, though simplistic, helps to explain the observed timing of the deceleration.