In many applications it is necessary to limit the vibrations of lightly damped shells by applying an optimal damping treatment that does not significantly increase the weight. This paper explores the partial coverage of cylindrical shells with a constrained viscoelastic damping layer, with emphasis on examining the minimum area of coverage that will yield optimal damping. The distribution of damping patches on the structure is based on strain energy intensity distribution maps derived for the purpose. The analysis uses the finite element method, and a suitable curved shell element is formulated for the add-on damping treatment. Numerical studies show that a partial coating procedure can be a viable approach in optimal damping designs.