  We investigate two techniques for controlling decoherence, focusing on the
crucial role played by the environmental spectrum. We show how environments
with different spectra lead to very different dynamical behaviours. Our study
clearly proves that such differences must be taken into account when designing
decoherence control schemes. The two techniques we consider are reservoir
engineering and quantum-Zeno control. We focus on a quantum harmonic oscillator
initially prepared in a nonclassical state and derive analytically its
non-Markovian dynamics in presence of different bosonic thermal environments.
On the one hand we show how, by modifying the spectrum of the environment, it
is possible to prolong or reduce the life of a Schr\"odinger cat state. On the
other hand we study the effect of nonselective energy measurements on the
degradation of quantumness of initial Fock states. In this latter case we see
that the crossover between Zeno (QZE) and anti-Zeno (AZE) effects, discussed by
Maniscalco et al. [Phys. Rev. Lett. 97, 130402 (2006)], is highly sensitive to
the details of the spectrum. In particular, for certain types of spectra, even
very small variations of the system frequency may cause a measurement-induced
acceleration of decoherence rather than its inhibition.
