2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101138In this paper, we study on knots and closed incompressible surfaces in the 3-sphere via Morse functions. We show that both of knots and closed incompressible surfaces can be isotoped into a "related Morse position" simultaneously. As an application, we have following results. *Smallness of Montesinos tangles with length two and Kinoshita's theta curve *Classification of closed incompressible and meridionally incompressible surfaces in 2-bridge theta-curve and handcuff graph complements and the complements of links which admit Hopf tangle decompositions.20 pages, 17 figures. This version (v6) is a final version to appear in J. Knot Theory and its RamificationsGeometric TopologyPrimary 57M25, 57M50; Secondary 57Q35, 57Q37text