A model of rods with heads of variable size, which are cofined to a planar surface, is used to study the influence of the head group size on tilted phases in Langmuir monolayers. Simple free energy considerations as well as exact zero temperature calculations indicate that molecules with small head groups tilt towards next nearest neighbors, and molecules with larger head groups towards nearest neighbors. This provides a possible explanation for recent experimental results, and for details of the generic phase diagram for fatty acid monolayers.