Full text can be accessed at http://link.springer.com/article/10.1007/s11786-007-0031-5Smooth 4-regular hamiltonian graphs are generalizations of cycle plus triangles graphs. It has been shown that both the independent set and 3-colorability problems are NP-Complete in this class of graphs. In this paper we show that these problems are fixed parameter tractable if we choose the number of inner cycles as parameter.