A multicore optical fiber includes two or more cores, a common interior cladding surrounding the two or more cores, and a common exterior cladding surrounding the common interior cladding. The common exterior cladding has a lower relative refractive index than the common interior cladding and reduces tunneling losses from the cores. The reduced tunneling loss allows placement of cores closer to the edge of the fiber, thus providing multicore optical fibers having higher core count for a given fiber diameter. Separation between cores is controlled to minimize crosstalk.