  The WMAP team has recently highlighted the usefulness of combining the
Ly-alpha forest constraints with those from the cosmic microwave background
(CMB). This combination is particularly powerful as a probe of the primordial
shape of the power spectrum. Converting between the Ly-alpha forest
observations and the linear mass power spectrum requires a careful treatment of
nuisance parameters and modeling with cosmological simulations. We point out
several issues which lead to an expansion of the errors, the two most important
being the range of cosmological parameters explored in simulations and the
treatment of the mean transmitted flux constraints. We employ a likelihood
calculator for the current Ly-alpha data set based on an extensive
6-dimensional grid of simulations. We show that the current uncertainties in
the mean transmission and the flux power spectrum define a degeneracy line in
the amplitude-slope plane. The CMB degeneracy due to the primordial power
spectrum shape follows a similar relation in this plane. This weakens the
statistical significance of the primordial power spectrum shape constraints
based on combined CMB+Ly-alpha forest analysis. Using the current data the
simplest n=1 scale invariant model with dn/dln k=0 and no tensors has a Delta
chi^2=4 compared to the best fitting model in which these 3 parameters are
free. Current data therefore do not require relaxing these parameters to
improve the fit.
