We perform broadband spin-wave spectroscopy on thin submicrometer-wide Ni80Fe20 magnetic wires. Intentionally, we apply the in-plane magnetic field under an angle that is a few degrees off with respect to the in-plane hard-axis direction. In an intermediate field regime we find dipole-exchange modes that, as substantiated by micromagnetic simulations, reflect spin waves in intrinsically formed nanometer-wide channels along the wire. Interestingly, this phenomenon is not ruled by the outer boundary conditions at the geometrical edges but by a deterministic zig-zag shaped magnetization configuration that varies on the nanometer scale in the inner part of the wire. In our case the individual channel width is only 65 nm, about a factor of five smaller than the geometrical width of 300 nm. Internal spin-wave guiding becomes possible, resembling the graded-index approach for optical wave guiding in fibers. This opens new perspectives for spin-wave propagation in magnonic waveguides.