We show that for every rooted, nitely branching, pruned tree T of height ! there exists a family F which consists of order isomorphic to T subtrees of the dyadic tree C = f0; 1g<N with the following properties: (i) the family F is a G subset of 2C; (ii) every perfect subtree of C contains a member of F; (iii) if K is an analytic subset of F, then for every perfect subtree S of C there exists a perfect subtree S0 of S such that the set fA 2 F : A S0g either is contained in or is disjoint from K. Our result simultaneously extends Louveau-Shelah-Velickovic theorem as well as Stern's theorem for broader classes of subtrees of the dyadic tree