The determination of the support of the equilibrium measure in the presence
of an external field is important in the theory of weighted polynomials on
the real line. Here we present a general condition guaranteeing that the s
upport consists of at most two intervals. Applying this to the external fie
lds associated with fast decreasing polynomials, we extend previous results
of Totik and Kuijlaars-Van Assche. In the proof we use the iterated balaya
ge algorithm which was first studied by Dragnev.