Slow evaporation of In from InP wafers has been investigated and identified as a major cause of surface roughness in thermal annealing and mass transport under sufficient phosphorus vapor protection. An analysis shows that In evaporation can be prevented by covering the wafer during the annealing process. However, the commonly used graphite cover by itself is inadequate protection because In vapor is able to permeate the graphite. On the other hand, InP covers alone result in problems caused by the mass transport that occurs between the InP wafer and cover. A covering scheme has been developed that uses InP covers and a quartz enclosure in addition to the graphite cover. This arrangement provides effective wafer protection permitting smooth wafer surfaces to be obtained reproducibly.