Isotherms and x-ray diffraction studies of eicosanoic acid Langmuir monolayers show a phase in which the molecular tilt is intermediate between nearest-neighbor (NN) and next-nearest-neighbor (NNN) directions. The transition from this "I" phase to an NN-tilted structure is first order, with a similar to 60 degrees change in the tilt direction, while the transition to an NNN-tilted structure is apparently continuous, These results can be explained using a Landau-type theory for uniaxially distorted lattices, which is a modification of an existing theory for hexagonal lattices [J.V. Selinger and D. R. Nelson, Phys. Rev. Lett. 61, 416 (1988)].