A two-layer Newtonian fluid model for muco-ciliary transport in the lung is developed where the viscosity of the upper mucous layer is very much greater than the viscosity of the lower periciliary layer. Theory is presented for both cases when the cilia penetrate, and do not penetrate, the very viscous mucous layer. Calculations suggest that, in normal circumstances, it is not essential for the cilia to penetrate the mucus to provide positive transport. However, it does suggest that there is a weak optimal penetration depth of the cilia of between 10-20% of the cilium length. In the case of high ciliary inactivity (e.g. 90% inactive), penetration of cilia into the mucus is essential for normal transport rates suggesting the mucociliary system may be deliberately overdesigned to cater for a whole range of pathological circumstances.