  The form of the primordial power spectrum has the potential to differentiate
strongly between competing models of perturbation generation in the early
universe and so is of considerable importance. The recent release of five years
of WMAP observations have confirmed the general picture of the primordial power
spectrum as deviating slightly from scale invariance with a spectral tilt
parameter of n_s ~ 0.96. Nonetheless, many attempts have been made to isolate
further features such as breaks and cutoffs using a variety of methods, some
employing more than ~ 10 varying parameters. In this paper we apply the robust
technique of Bayesian model selection to reconstruct the optimal degree of
structure in the spectrum. We model the spectrum simply and generically as
piecewise linear in ln k between `nodes' in k-space whose amplitudes are
allowed to vary. The number of nodes and their k-space positions are chosen by
the Bayesian evidence so that we can identify both the complexity and location
of any detected features. Our optimal reconstruction contains, perhaps,
surprisingly few features, the data preferring just three nodes. This
reconstruction allows for a degree of scale dependence of the tilt with the
`turn-over' scale occuring around k ~ 0.016 Mpc^{-1}. More structure is
penalised by the evidence as over-fitting the data, so there is currently
little point in attempting reconstructions that are more complex.
