  We investigate the accuracy of slow-roll inflation in light of current
observational constraints, which do not allow for a large deviation from scale
invariance. We investigate the applicability of the first and second order
slow-roll approximations for inflationary models, including those with large
running of the scalar spectral index. We compare the full numerical solutions
with those given by the first and second order slow-roll formulae. We find that
even first order slow-roll is generally accurate; the largest deviations arise
in models with large running where the error in the power spectrum can be at
the level of 1-2%. Most of this error comes from inaccuracy in the calculation
of the slope and not of the running or higher order terms. Second order
slow-roll does not improve the accuracy over first order. We also argue that in
the basis $\epsilon_0=1/H$, $\epsilon_{n+1}={d\ln|\epsilon_n|}/{dN}$,
introduced by Schwarz et al. (2001), slow-roll does not require all of the
parameters to be small. For example, even a divergent $\epsilon_3$ leads to
finite solutions which are accurately described by a slow-roll approximation.
Finally, we argue that power spectrum parametrization recently introduced by
Abazaijan, Kadota and Stewart does not work for models where spectral index
changes from red to blue, while the usual Taylor expansion remains a good
approximation.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory