An approximate analytical solution for tube-coating wire with a highly viscous Newtonian fluid is developed (high Froude and capillary numbers). Acute extrusion angles for the annular slit are considered. We obtain expressions for the melt cone shape, coating thickness, contact length, contact pressure, drawing force, apparent contact angle, and contact convexity. In this article, we identify a process indeterminacy that arises in classical tube coating which employs a parallel annulus, and this necessitates applying an internal vacuum. We show that with a rapidly converging extrusion annulus, this indeterminacy vanishes and so does the need for an internal vacuum. Thus, a unique solution for the contact length is always obtained. The extension to a viscoelastic fluid is also briefly considered.