Propagation of bound plasmon-polariton modes along 30-nm-thin gold strips on a silica substrate at the free-space wavelength of 1500 nm is investigated both theoretically and experimentally when decreasing the strip width from 1500 nm down to the aspect-ratio limited width of 30 nm, which ensures deep subwavelength mode confinement. The main mode characteristics (effective mode index, propagation length, and mode profile) are determined from the experimental amplitude- and phase-resolved near-field images for various strip widths (from 30 to 1500 nm), and compared to numerical simulations. The mode supported by the narrowest strip is found to be laterally confined within ~ 100 nm at the air side, indicating that the realistic limit for radiation nanofocusing in air using tapered metal strips is ~ λ/15.