We present a simple method for fitting parametrized mass models of the Milky Way to observational constraints. We take a Bayesian approach which allows us to take into account input from photometric and kinematic data, and expectations from theoretical modelling. This provides us with a best-fitting model, which is a suitable starting point for dynamical modelling. We also determine a probability density function on the properties of the model, which demonstrates that the mass distribution of the Galaxy remains very uncertain. For our choices of parametrization and constraints, we find disc scalelengths of 3.00 ± 0.22 and 3.29 ± 0.56 kpc for the thin and thick discs, respectively, a solar radius of 8.29 ± 0.16 kpc and a circular speed at the Sun of 239 ± 5 km s−1, a total stellar mass of 6.43 ± 0.63 × 1010 M⊙, a virial mass of 1.26 ± 0.24 × 1012 M⊙ and a local dark matter density of 0.40 ± 0.04 GeV cm−3. We find some correlations between the best-fitting parameters of our models (for example, between the disc scalelengths and the solar radius), which we discuss. The chosen disc scaleheights are shown to have little effect on the key properties of the model.