  Let $f(x)$ be a separable polynomial over a local field. Montes algorithm
computes certain approximations to the different irreducible factors of $f(x)$,
with strong arithmetic properties. In this paper we develop an algorithm to
improve any one of these approximations, till a prescribed precision is
attained. The most natural application of this "single-factor lifting" routine
is to combine it with Montes algorithm to provide a fast polynomial
factorization algorithm. Moreover, the single-factor lifting algorithm may be
applied as well to accelerate the computational resolution of several global
arithmetic problems in which the improvement of an approximation to a single
local irreducible factor of a polynomial is required.
