Single metallic nanorods acting as half-wave antennas in the optical range exhibit an asymmetric, multi-resonant scattering spectrum that strongly depends on both their length and dielectric properties. Here we show that such spectral features can be easily understood in terms of Fano-like interference between adjacent plasmon resonances. On the basis of analytical and numerical results for different geometries, we demonstrate that Fano resonances may appear for such single-particle nanoantennas provided that interacting resonances overlap in both spatial and frequency domains.