Copolymers of styrene and maleic acid (SMA) have gained great attention as alternatives to conventional detergents, as they offer decisive advantages for studying membrane proteins and lipids in vitro. These polymers self-insert into artificial and biological membranes and, at sufficiently high concentrations, solubilise them into disc-shaped nanostructures containing a lipid bilayer core surrounded by a polymer belt. We have used (31)P nuclear magnetic resonance spectroscopy and dynamic light scattering to systematically study the solubilisation of vesicles composed of saturated or unsaturated phospholipids by an SMA copolymer with a 3 : 1 styrene/maleic acid molar ratio at different temperatures. Solubilisation was thermodynamically rationalised in terms of a three-stage model that treats various lipid/polymer aggregates as pseudophases. The solubilising capacity of SMA(3 : 1) towards a saturated lipid is higher in the gel than in the liquid-crystalline state of the membrane even though solubilisation is slower. Although the solubilisation of mixed fluid membranes is non-selective, the presence of a non-bilayer phospholipid lowers the threshold at which the membrane becomes saturated with SMA(3 : 1) but raises the polymer concentration required for complete solubilisation. Both of these trends can be explained by considering the vesicle-to-nanodisc transfer free energies of the lipid and the polymer. On the basis of the phase diagrams thus obtained, re-association of polymer-solubilised lipids with vesicles is possible under mild conditions, which has implications for the reconstitution of proteins and lipids from nanodiscs into vesicular membranes. Finally, the phase diagrams provide evidence for the absence of free SMA(3 : 1) in vesicular lipid suspensions.