The false liquid-liquid splits that often occur when modelling polar-nonpolar binary mixtures can be avoided in most cases by either including upper critical solution points (UCSPs) in the fit, or by using a constrained fit. Including UCSPs in the fit gives a better control of how the region of false liquid-liquid splits is shifted including a correct pressure dependence if UCSPs are known at more than one pressure. A constrained fit can only guarantee that the region of false liquid-liquid splits is shifted away from the region of the experimental VLE data. When there are more than one parameter in the mixing rule, two constraints are needed to avoid oscillations in the numerical process. Avoiding instability leads to a worse fit of the VLE data. The methods are illustrated on fits of five mixtures of methanol + n-alkane using the Patel-Teja EOS with association, and on predictions of one ternary mixture.