In the design of power reactors containing lattices of fuel rods in liquid coolant, it would be useful to employ cell-averaged transport parameters reflecting anisotropic neutron migration when this is significant. Measurements and Monte Carlo calculations of anisotropic neutron migration are described for rod lattices. The well-known flux peaking near thin sources is found to be accompanied by thin source effects on migration areas. Situations of substantial migration anisotropy and thin source effects are delimited.