We have found that InxGa(1-x)N/GaN multi-quantum-well (MQW) light emitting diodes (LEDs) having periodic thickness variation (TV) in InxGa(1-x)N active layers exhibit substantially higher optical efficiency than LEDs with uniform InxGa(1-x)N layers. In these nano-structured LEDs, the thickness variation of the active layers is shown to be more important than In composition fluctuation in quantum confinement of excitons (carriers). Detailed STEM-Z contrast analysis, where image contrast is proportional to Z2 (atomic number)2, was carried out to investigate the thickness variation as well as the spatial distribution of In. In the nanostructured LEDs, there are short-range (SR-TV, 3 to 4 nm) and long-range thickness variations (LR-TV, 50 to 100 nm) in InxGa(1-x)N layers. It is envisaged that LR-TV is the key to quantum confinement of the carriers and enhancing the optical efficiency. We propose that the LR-TV thickness variation is caused by two-dimensional strain in the InxGa(1-x)N layer below its critical thickness. The SR-TV may be caused by In composition fluctuation. The observations on thickness variation are in good agreement with model calculations based upon strain effects.