  We study a novel S=1/2 cluster chain Hamiltonian which has recently been
proposed in the context of the charge ordered low-temperature phase of
alpha'-NaV2O5. We perform a detailed investigation of this model within a large
range of parameters using perturbation theory and Lanczos diagonalization.
Using model-specific local conservation laws and parameter-dependent mappings
to various effective low-energy Hamiltonians we uncover a rich phase diagram
and several regimes of gapful spin-excitations. We find that the overall
features of recent neutron scattering data on alpha'-NaV2O5 can be fitted
within this model, however using a set of parameters which seems unlikely.
