The observation of lateral phase separation in lipid bilayers has received considerable attention, especially in connection to lipid raft phenomena in cells. It is widely accepted that rafts play a central role in cellular processes, notably signal transduction. While micrometer-sized domains are observed with some model membrane mixtures, rafts much smaller than 100 nm-beyond the reach of optical microscopy-are now thought to exist, both in vitro and in vivo. We have used small-angle neutron scattering, a probe free technique, to measure the size of nanoscopic membrane domains in unilamellar vesicles with unprecedented accuracy. These experiments were performed using a four-component model system containing fixed proportions of cholesterol and the saturated phospholipid 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC), mixed with varying amounts of the unsaturated phospholipids 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We find that liquid domain size increases with the extent of acyl chain unsaturation (DOPC:POPC ratio). Furthermore, we find a direct correlation between domain size and the mismatch in bilayer thickness of the coexisting liquid-ordered and liquid-disordered phases, suggesting a dominant role for line tension in controlling domain size. While this result is expected from line tension theories, we provide the first experimental verification in free-floating bilayers. Importantly, we also find that changes in bilayer thickness, which accompany changes in the degree of lipid chain unsaturation, are entirely confined to the disordered phase. Together, these results suggest how the size of functional domains in homeothermic cells may be regulated through changes in lipid composition.