  An experimental realization of high-precision direct frequency comb
spectroscopy using counter-propagating femtosecond pulses on two-photon atomic
transitions is presented. Doppler broadened background signal, hampering
precision spectroscopy with ultrashort pulses, is effectively eliminated with a
simple pulse shaping method. As a result, all four 5S-7S two-photon transitions
in a rubidium vapor are determined with both statistical and systematic
uncertainties below 10$^{-11}$, which is an order of magnitude better than
previous experiments on these transitions.
