Sco X-1 is a low-mass X-ray binary (LMXB) that has one of the most precisely determined set of binary parameters such as the mass accretion rate, companions mass ratio and the orbital period. For this system, as well as for a large fraction of other well-studied LMXBs, the observationally-inferred mass accretion rate is known to strongly exceed the theoretically expected mass transfer rate. We suggest that this discrepancy can be solved by applying a modified magnetic braking prescription, which accounts for increased wind mass loss in evolved stars compared to main sequence stars. Using our mass transfer framework based on {tt MESA}, we explore a large range of binaries at the onset of the mass transfer. We identify the subset of binaries for which the mass transfer tracks cross the Sco X-1 values for the mass ratio and the orbital period. We confirm that no solution can be found for which the standard magnetic braking can provide the observed accretion rates, while wind-boosted magnetic braking can provide the observed accretion rates for many progenitor binaries that evolve to the observed orbital period and mass ratio.