Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to stochastic fluctuations of allele frequencies above and beyond genetic drift - an effect known as genetic draft. Since recombination disrupts associations between alleles, draft is strong when recombination is rare. Here, we study a facultatively outcrossing population in a regime where the frequency of out-crossing and recombination, r, is small compared to the characteristic scale of fitness differences \sigma. In this regime, fit genotypes expand clonally, leading to large fluctuations in the number of recombinant offspring genotypes. The power law tail in the distribution of the latter makes it impossible to capture the dynamics of draft by an effective neutral model. Instead, we find that the fixation time of a neutral allele increases only slowly with the population size but depends sensitively on the ratio r/\sigma. The efficacy of selection is reduced dramatically and alleles behave "quasi-neutrally" even for Ns>> 1, provided that |s|< s_c, where s_c depends strongly on r/\sigma, but only weakly on population size N. In addition, the anomalous fluctuations due to draft change the spectrum of (quasi)-neutral alleles from f(\nu)\sim 1/\nu, corresponding to drift, to \sim1/\nu^2. Finally, draft accelerates the rate of two step adaptations through deleterious intermediates.