Bounded type Siegel disks of finite type maps with few singular values

Let U be an open subset of the Riemann sphere (hat {mathbb{C}}). We give sufficient conditions for which a finite type map f: U → (hat {mathbb{C}}) with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-?wi?tek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-?wi?tek.