Abstract: A single mode optical fiber comprises a core, a first cladding surrounding the core, and a second cladding surrounding the first cladding. It also comprises a third cladding region (or index "ring"). The core, has radius a and refractive index n.sub.c, the first, second, and third cladding regions have inner radii, R.sub.1i, R.sub.2i, and R.sub.3i, outer radii R.sub.1o, R.sub.2o, and R.sub.3o, and indices n.sub.1, n.sub.2, n.sub.3, respectively. The fiber has n.sub.1 <n.sub.3, R.sub.1o .ltoreq.R.sub.3i, R.sub.3o .ltoreq.R.sub.2i. In preferred embodiments, a=R.sub.1i, R.sub.1o =R.sub.3i, R.sub.3o =R.sub.2i. Appropriate choice of ring parameters can result in a lowering of the cut-off wavelength of the fiber, or in fiber that is less sensitive to macrobending than similar prior art fiber lacking an index ring, without substantial change in fiber parameters that depend primarily on the waveform in the core. An optical fiber communications system comprising the inventive fiber is also disclosed.