  We design realizable time-dependent semiclassical pulses to invert the
population of a two-level system faster than adiabatically when the
rotating-wave approximation cannot be applied. Different approaches, based on
the counterdiabatic method or on invariants, may lead to singularities in the
pulse functions. Ways to avoid or cancel the singularities are put forward when
the pulse spans few oscillations. For many oscillations an alternative
numerical minimization method is proposed and demonstrated.
