Social Security benefits may be commenced at any time between ages 62 and 70.  As individuals who claim later can, on average, expect to receive benefits for a shorter period, an actuarial adjustment is made to the monthly benefit amount to reflect the age at which benefits are claimed.  In earlier work (Shoven and Slavov, 2012), we investigated the actuarial fairness of this adjustment for individuals with average life expectancy for their cohort.  We found that for plausible real interest rates, delaying is actuarially advantageous for a large subset of people, particularly for primary earners in married couples.  In this paper, we quantify the degree of actuarial advantage or disadvantage for individuals whose mortality differs from the average.  We find that at interest rates close to zero, most households – even those with mortality rates that are twice the average – benefit from some degree of delay, at least for the primary earner.  At real interest rates closer to their historical average, however, singles with mortality that is substantially greater than average do not benefit from delay; however, primary earners with high mortality can still improve the present value of the household’s benefits through delay.  We also investigate the extent to which the actuarial advantage of delay has grown since the early 1960s, when the choice of when to claim first became available, and we decompose this growth into three effects: (1) the effect of changes in Social Security's rules, (2) the effect of changes in the real interest rate, and (3) the effect of changes in life expectancy.