  We show how additional constraints, restricting the spectrum of the optimized
pulse or confining the system dynamics, can be used to steer optimization in
quantum control towards distinct solutions. Our examples are multi-photon
excitation in atoms and vibrational population transfer in molecules. We show
that a spectral constraint is most effective in enforcing non-resonant
two-photon absorption pathways in atoms and avoiding unnecessarily broad
spectra in Raman transitions in molecules. While a constraint restricting the
system to stay in an allowed subspace is also capable of identifying
non-resonant excitation pathways, it does not avoid spurious peaks in the pulse
spectrum. Both constraints are compatible with monotonic convergence but imply
different additional numerical costs.
