It is know that the Valdivia compact spaces can be characterized by a special family of retractions called r-skeleton (see [10]). Also we know that there are compact spaces with r-skeletons which are not Valdivia. In this paper, we shall study r-skeletons and special families of closed subsets of compact spaces. We prove that if X is a zero-dimensional compact space and {rs:s∈Γ} is an r-skeleton on X such that |rs(X)|≤ω for all s∈Γ, then X has a dense subset consisting of isolated points. Also we give conditions to an r-skeleton in order that this r-skeleton can be extended to an r-skeleton on the Alexandroff Duplicate of the base space. The standard definition of a Valdivia compact spaces is via a Σ-product of a power of the unit interval. Following this fact we introduce the notion of π-skeleton on a compact space X by embedding X in a suitable power of the unit interval together with a pair (F,φ), where F is family of metric separable subspaces of X and φ an ω-monotone function which satisfy certain properties. This new notion generalize the idea of a Σ-product. We prove that a compact space admits a r-skeleton iff it admits a π-skeleton. This equivalence allows to give a new proof of the fact that the product of compact spaces with r-skeletons admits an r-skeleton (see [9]).