More than 50 years after the dawn of X-ray astronomy, the dynamical parameters of the prototypical X-ray binary Sco X-1 are still unknown. We combine a Monte Carlo analysis, which includes all the previously known orbital parameters of the system, along with the K-correction to set dynamical constraints to the masses of the compact object (M1 < 1.73 M⊙) and the companion star (0.28 M⊙ < M2 < 0.70 M⊙). For the case of a canonical neutron star mass of M1 ˜ 1.4 M⊙, the orbital inclination is found to be lower than 40°. We also present the best near-infrared spectrum of the source to date. There is no evidence of donor star features on it, but we are able to constrain the veiling factor as a function of the spectral type of the secondary star. The combination of both techniques restricts the spectral type of the donor to be later than K4 and luminosity class IV. It also constrains the contribution of the companion light to the infrared emission of Sco X-1 to be lower than 33 per cent. This implies that the accretion related luminosity of the system in the K band is larger than ˜4 × 1035 erg s-1.