Experimental data from the Trident Laser facility is presented showing quasimonoenergetic carbon ions from nm-scaled foil targets with an energy spread of as low as ±15% at 35 MeV. These results and high-resolution kinetic simulations show laser acceleration of quasimonoenergetic ion beams by the generation of ion solitons with circularly polarized laser pulses (500 fs, λ=1054 nm). The conversion efficiency into monoenergetic ions is increased by an order of magnitude compared with previous experimental results, representing an important step towards applications such as ion fast ignition.