The solubility of water in melts in the NaAl-Si3O8 - H2O system at high P and T was deduced from the appearance of quenched products and from water concentrations in the quenched glasses measured by ion probe, calibrated by hydrogen manometry. Starting materials were gels with sufficient water added to ensure saturation of the melts under the run conditions. Experiments were carried out for 10-30 h in an internally heated argon pressure vessel (eight at 1400-degrees-C and 0.2-0.73 GPa and three at 0.5 GPa and 900-1200-degrees-C) and for 1 h in a piston-cylinder apparatus (three at 1200-degrees-C, 1-1.3 GPa). No bubbles were observed in the glasses quenched at P < 0.5 GPa or from T < 1300-degrees-C at 0.5 GPa. Bubble concentration in glasses quenched from 1400-degrees-C was low at 0.5, moderate at 0.55 GPa and very high at 0.73 GPa and still higher in glasses quenched in the piston cylinder. Water concentration was measured in all glasses, except for the one at 0.55 GPa, for which it was only estimated, and for those at greater-than-or-equal-to 0.73 GPa because bubble concentration was too high. Inferred water solubilities in the melt increase strongly with increasing P at 1400-degrees-C (from 6.0 wt% at 0.2 GPa to approximately 15 at 0.55 GPa) and also with increasing Tat 0.5 GPa (from 9.0 wt% at 900-degrees-C to approximately 12.9 at 1400-degrees-C). The T variation of water solubility is fundamental for understanding the behaviour of melts on quenching. If the solubility decreases with T at constant P (retrograde solubility), bubbles cannot form by exsolution on isobaric quenching, whereas if the solubility is prograde they may do so if the cooling rate is not too fast. It is inferred from observed bubble concentrations and from our and previous solubility data that water solubility is retrograde at low P and prograde at and above approximately 0.45 GPa; it probably changes with T from retrograde below to prograde above approximately 900-degrees-C at 0.5 GPa. Moreover, the solubility is very large at higher pressures (possibly > approximately 30 wt% at 1.3 GPa and 1200-degrees-C) and critical behaviour is approached at approximately 1.3 GPa and 1200-degrees-C. The critical curve rises to slightly higher P at lower T and intersects the three-phase or melting curve at a critical end point near 670-degrees-C and 1.5 GPa, above which albite coexists only with a supercritical fluid.