This paper discusses the current drive efficiency by the combined action of EC and LH waves in the presence of a dc electric field and transport, with an internal transport barrier. The transport is assumed to be produced by magnetic fluctuations. The study explores the different barrier parameters and their influence on the current drive efficiency. We study the subject by numerically solving the Fokker–Planck equation. Our main result is that the barrier depth and barrier width are important to determine the correct shape of the current density profile but not to determine the current drive efficiency, which is very little influenced by these parameters. We also found similar results for the influence of the level of magnetic fluctuations on the current density profile and on the current drive efficiency.