  Recent cosmological observations hint at a deviation from the simple
power-law form of the primordial spectrum of curvature perturbations. In this
paper we show that in the presence of a tensor component, a turn-over in the
initial spectrum is preferred by current observations, and hence non-power-law
models ought to be considered. For instance, for a power-law parameterisation
with both a tensor component and running parameter, current data show a
preference for a negative running at more than $2.5\sigma$ C.L. As a
consequence of this deviation from a power-law, constraints on the
tensor-to-scalar ratio $r$ are slightly broader. We also present constraints on
the inflationary parameters for a model-independent reconstruction and the
Lasenby & Doran (LD) model. In particular, the constraints on the
tensor-to-scalar ratio from the LD model are: $r_{\rm LD}=0.11\pm{0.024}$. In
addition to current data, we show expected constraints from Planck-like and
CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling
chains. For all the models, we have included the Bayesian Evidence to perform a
model selection analysis. The Bayes factor, using current observations, shows a
strong preference for the LD model over the standard power-law
parameterisation, and provides an insight into the accuracy of differentiating
models through future surveys.
