Using high resolution superconducting quantum interference device magnetometry we have made detailed measurements of the waiting time effect of the thermoremanent magnetization (TRM) decays on a single-crystal CuMn(6%) spin-glass sample near T-g. We have systematically mapped the rapid decrease of the characteristic timescale tw(eff), approaching T-g from below, for waiting times ranging from 100 to 100 000 s. Using tw(eff) to determine the length scale of the growth of correlations during the waiting time, xi(TRm) (observed in both numerical studies and experiment), we observe both growth of xi(TRm) in the spin-glass phase and then a rapid reduction very close to T-g. We interpret this reduction in xi(TRm), for all waiting times, as being governed by the critical correlation length scale delta(cr)(it) = a(T - T-c)(-nu).