  We revisit the problem of switching off unwanted phase evolution and
decoherence in a single two-state quantum system in the light of recent results
on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett.
{\bf 94}, 060502 (2005)]. A systematic comparison with standard cyclic
decoupling is effected for a variety of dynamical regimes, including the case
of both semiclassical and fully quantum decoherence models. In particular,
exact analytical expressions are derived for randomized control of decoherence
from a bosonic environment. We investigate quantitatively control protocols
based on purely deterministic, purely random, as well as hybrid design, and
identify their relative merits and weaknesses at improving system performance.
We find that for time-independent systems, hybrid protocols tend to perform
better than pure random and may improve over standard asymmetric schemes,
whereas random protocols can be considerably more stable against fluctuations
in the system parameters. Beside shedding light on the physical requirements
underlying randomized control, our analysis further demonstrates the potential
for explicit control settings where the latter may significantly improve over
conventional schemes.
