  We investigate the coherent control of the photo\-electron angular
distribution in bichromatic atomic ionization. Neon is selected as target since
it is one of the most popular systems in current gas-phase experiments with
free-electron lasers (FELSs). In particular, we tackle practical questions,
such as the role of the fine-structure splitting, the pulse length, and the
intensity. Time-dependent and stationary perturbation theory are employed, and
we also solve the time-dependent Schr\"odinger equation in a single-active
electron model. We consider neon ionized by a FEL pulse whose fundamental
frequency is in resonance with either $2p-3s$ or $2p-4s$ excitation. The
contribution of the non\-resonant two-photon process and its potential
constructive or destructive role for quantum coherent control is investigated.
