  The scalar spectral index n is an important parameter describing the nature
of primordial density perturbations. Recent data, including that from the WMAP
satellite, shows some evidence that the index runs (changes as a function of
the scale k at which it is measured) from n>1 (blue) on long scales to n<1
(red) on short scales. We investigate the extent to which inflationary models
can accomodate such significant running of n. We present several methods for
constructing large classes of potentials which yield a running spectral index.
We show that within the slow-roll approximation, the fact that n-1 changes sign
from blue to red forces the slope of the potential to reach a minimum at a
similar field location. We also briefly survey the running of the index in a
wider class of inflationary models, including a subset of those with
non-minimial kinetic terms.
