  The study of the decoherence of qubits in spin systems is almost restricted
to environments whose constituents are spin-$\frac{1}{2}$ particles. In this
paper we consider environments that are composed of particles of higher spin,
and we investigate the consequences on the dynamics of a qubit coupled to such
baths via Heisenberg $XY$ and Ising interactions. It is shown that while the
short time decay in both cases gets faster as the magnitude of the spin
increases, the asymptotic behavior exhibits an improvement of the suppression
of the decoherence when the coupling is through Heisenberg $XY$ interactions.
In the case of a transverse Ising model, we find that the mean field
approximation breaks down for high values of the spin.
