  We study the decoherence of a central spin-1/2 due to a closed environment
composed of spin-1/2 particles. It is known that a frustrated spin environment,
such as a spin glass, is much more efficient for decoherence of the central
spin than a similar size environment without frustration. We construct a
Hamiltonian where the degree of frustration is parametrized by a single
parameter $\kappa$. By use of this model we find that the environment can be
classified by two distinct regimes with respect to the strength of level
repulsion. These regimes behave qualitatively different with respect to
decoherence of the central spin and might explain the strong enhancement of
decoherence observed for frustrated environments.
