  We introduce a method where successive coordinate transformations are applied
to decrease the error in the adiabatic master equation resulting from
truncation in the local adiabatic parameter. Our method reduces the nonphysical
behaviour stemming from the lack of complete positivity. The strong
environment-induced relaxation at high Cooper pair pumping frequencies leads to
adiabatic ground-state pumping only in the lowest-order approximation. We
illustrate the robustness of the frequency where the adiabaticity breaks down
using the high-order theory and show the emergence of an optimal environmental
coupling strength, for which ideal pumping is preserved for the highest
frequency. Finally, we study the effect of quantum interference on the pumped
current and give an estimate for the relaxation rate of an experimentally
measured system.
