Longitudinal Gompertzian analysis yields the counterintuitive conclusion that an improved environment can cause a decrease in maximum lifespan. The basis for this conclusion is examined. Results include the following: 1) The use of a specified high mortality rate as a criterion for maximum lifespan is arbitrary and leads to a calculated lifespan which is quite sensitive to the value of the criterion. 2) The definition of lifespan as the age to which a specified small population fraction survives is less arbitrary and less sensitive to the chosen criterion value. 3) However, the use of a survival criterion for lifespan in place of a mortality-rate criterion does not eliminate the seeming contradiction between environmental improvement and decreased lifespan. 4) Mortality rates can be approximated in semilogarithmic coordinates by three straight-line segments. The first segment, applicable through age 85, is the conventional Gompertz function. The second segment, representing ages 85 through 96, has a lower slope than the first, while the third segment, representing ages 96 through 124, has a negative slope. 5) The mortality rate obtained by extrapolating the first segment to a nominal age of maximum lifespan differs markedly from the true mortality rate at that age. 6) The conclusion that an improved environment is associated with a reduction in lifespan arises as a consequence of such an extrapolation.