  We discuss the commonly encountered problem when optimizing NMR pulses using
optimal control that the otherwise very precise NMR theory does not provide as
excellent agreement with experiments. We hypothesize that this disagreement is
due to phase transients in the pulse due to abrupt phase- and amplitude changes
resulting in a large bandwidth. We apply the GROUP algorithm that gives high
fidelity pulses with a low bandwidth compared to the typical GRAPE pulses. Our
results obtain a better agreement between experiment and simulations supporting
our hypothesis and solution to the problem.
