  Driving a certain transition without including undesired transitions is an
ubiquitous problem in quantum control and the implementation of quantum
information processing. This problem gets the more challenging the weaker the
desired transition couples to the control field, and the denser the system's
spectrum is. With the explicit example of a trapped ion we show how temporally
shaped driving helps to increase the fidelity of a gate operation beyond the
regular spectral selection of resonantly driven transitions. We chose the
explicit example of side-band transitions, since those couple more weakly to a
control field than carrier transitions. Driving a sideband transition without
carrier excitation thus allows us to test the limits of frequently employed
control tools, and we discuss their potential and limitations.
