Tubed incompressible surfaces in knot and link complements

We prove that the complements of all knots and links in S3 which have a 2n-plat projection with absolute value of all twist coefficients bigger than 2 contain closed embedded incompressible non-boundary parallel surfaces. These surfaces are obtained from essential planar meridional surfaces by tubing to one side along the knot or link. In the case of a knot it follows that these surfaces stay incompressible in all manifolds obtained by non-trivial surgery on the knot.