Let S be the set of rational or irrational numbers whose continued fractions have coefficients greater than the Inou Shishikura constant. Let Se be the subset of those which are of bounded type. I will show that if θ0 ∈ Se, as θ tends to θ0 within S, the limit superior of the postcritical set of Pθ : z 7→ e2iπθz + z 2 is contained in the closure of the Siegel disk of Pθ0.