The cononsolvency effect of poly(N-isopropylacrylamide) (PNIPAM) in a mixture of water and methanol is investigated at variable temperatures (similar to 20-50 degrees C) and pressures (0.1-265 MPa) using small-angle neutron scattering (SANS). The phase diagram is mapped out by turbidimetry, demonstrating that the solubility range is hugely extended with pressure as compared to that of pure water. In the one-phase state, SANS over the q range from 0.015 to 2.2 nm(-1) on the solution in water/methanol revealed concentration fluctuations at small length scales. These show critical behavior; however, the critical exponents are far smaller than predicted by mean-field theory, which may be related to large-scale inhomogeneities observed already in the one-phase state. From the correlation length, the effective Flory-Huggins interaction parameter between the PNIPAM segments and the solvent mixture is determined as a function of pressure. Upon heating through the cloud point, the large-scale inhomogeneities transform into mesoglobules with smooth surfaces, while the width of the transition increases with pressure.