  We give a new proof of the following conjecture of Yoccoz: the sum of the
logarithm of the conformal radius of fixed Siegel disks of monic quadratic
polynomials and of the Brjuno function of their rotation number is bounded from
above.
  In a former article we obtained a first proof based on the control of
parabolic explosion. Here, we present a more elementary proof based on Yoccoz's
initial methods.
  We then extend this result to some new families of polynomials such as
unicritical ones. We also show that the conjecture does not hold for some other
families of polynomials.
