Phase-matched four-wave mixing in higher-order modes of microstructure fibers allows unprecedentedly high efficiencies of anti-Stokes frequency conversion to be achieved for subnanojoule femtosecond laser pulses. 70-fs pulses of 790-nm radiation were used to generate an anti-Stokes component at 520-530 nm in a higher-order mode of a microstructure fiber with a 4.8-microm core. The maximum ratio of the anti-Stokes signal energy to the energy of the pump component in the output spectrum is estimated as 1.7.