The segment structure of 1-monopalmitoylglycerol monolayer domains at the air-water interface studied by Brewster angle microscopy is related to the results of X-ray diffraction measurements as a function of surface pressure. The condensed-phase domains are subdivided into seven segments and have segment angles near 52 degrees. The segment boundaries are ascribed to low-energy lattice rows which are the [31] and the [3 $($) over bar$$ 1] lines in the two-dimensional lattice. As the lattice structure is changed upon compression, shifting the angle between these directions toward 58 degrees, 7-fold segment structures are expected to transform into 6-fold ones on compression to high surface pressures. This is observed, supporting the validity of the model, although the aliphatic tails form a free rotator phase and no crystal.