  We investigate ways to optimize adiabaticity and diabaticity in the
Landau-Zener model with non-uniform sweeps. We show how diabaticity can be
engineered with a pulse consisting of a linear sweep augmented by an
oscillating term. We show that the oscillation leads to jumps in populations
whose value can be accurately modeled using a model of multiple,
photon-assisted Landau-Zener transitions, which generalizes work by Wubs et al.
[New J. Phys. 7, 218 (2005)]. We extend the study on diabaticity using methods
derived from optimal control. We also show how to preserve adiabaticity with
optimal pulses at limited time, finding a non-uniform quantum speed limit.
