2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221920We present a short elementary proof of an existence theorem of certain CAT(-1)-surfaces in open hyperbolic 3-manifolds. The main construction lemma in Calegari and Gabai's proof of Marden's Tameness Conjecture can be replaced by an applicable version of our theorem.This is the version published by Geometry & Topology on 12 September 2006Geometric Topology57M50, 30F40text