A multiwave stochastic parameterization of nonorographic gravity waves (GWs), representing GWs produced by convection and a background of GWs in the midlatitudes, is tuned and tested against momentum fluxes derived from long-duration balloon flights. The tests are done offline using data sets corresponding to the Southern Ocean during the Concordiasi campaign in 2010. We also adopt the limiting constraint that the drag produced by the scheme resembles that produced by a highly tuned spectral GW parameterization, the so-called Hines scheme. Our results show that the parameterization can reproduce the momentum flux intermittency measured during the campaign, which is relevant since it strongly impacts on the vertical distribution of the GW drag. We also show that, at the altitude of the balloon flights, the momentum flux intermittency is in good part due to the GW sources: filtering by the background winds only becomes effective at much higher altitude. These results are based on bulk formulae for the GW momentum flux that could be used to replace our background GWs by GWs produced by fronts. Finally, the GW energy spectra built out of the stochastic scheme by averaging over a large ensemble of realizations are comparable to the classical vertical spectra of GWs, used today in globally spectral schemes. This indicates that multiwave and spectral schemes can be reconciled once a stochastic approach is used.