It is generally believed that inflationary models for the origin of pr
imordial density perturbations predict a spectral index n less than or
equal to 1. However, some observations, such as the first two years o
f COBE data, the Tenerife temperature anisotropy detection, bulk motio
ns, and structures on the similar to 50h(-1) Mpc scale, have recently
aroused much interest in spectral indices n > 1 (''blue spectra''). We
show that there is a class of inflationary models leading to this kin
d of spectra: they are produced while the inflaton field rolls down to
a potential minimum with the potential energy dominated by a cosmolog
ical-constant-like piece.