The potential physiological relevance of liquid-liquid phase separation in lipid membranes to the formation and stability of "lipid rafts" in cellular plasma membranes has prompted extensive investigation of the physical chemistry underlying these phenomena. In this contribution, the line tension (gamma) and dipole density differences ( micro) between demixed fluid phases of monolayers comprised of dimyristoylphosphatidylcholine (DMPC) and dihydrocholesterol (DChol) were investigated by measuring the two-dimensional thermal fluctuations of domain boundaries visualized by the inclusion of a fluorescent tracer lipid. These parameters are essential determinants of domain stability, and their quantification will yield an increased understanding of the physical processes responsible for aspects of lateral phase separation. Employing an extensive data set, the surface pressure dependence of gamma and mu was determined at three different monolayer compositions (30%, 35%, and 40% DChol). Both parameters were found to decrease with a power law dependence as the surface pressure approached the phase transition pressure (pi t), in agreement with previous measurements. Additionally, photobleaching effects and domain size influence were quantified and found to be small in our system. We suggest that the method of flicker spectroscopy can be helpful in identifying line-active compounds.