  In recent papers we have introduced a method for the study of limit cycles of
the Lienard system: dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial.
The method gives a sequence of polynomials R_n(x), whose roots are related to
the number and location of the limit cycles, and a sequence of algebraic
approximations to the bifurcation set of the system. In this paper, we present
a variant of the method that gives very important qualitative and quantitative
improvements.
