Health of migrants is a widely studied topic. It has been argued that migrant health may deteriorate over time. Though migrants are a "hard to reach" population in survey data, this paper builds on a unique dataset provided by Médecins du Monde from five countries. We study self-perceived health (SPH) in connection with socioeconomic and demographic factors and length of stay. Results differ for men and women. Compared to other documented migrants, asylum seekers have a 50-70% greater chance of having worse health. Migrants with better living conditions have a 57-78% chance of being in better health. Male migrants with a job have between a 82-116% chance of being in good health. The probability for women from poorer countries to have a better physical SPH after three months of residing in the host country is six-fold that of women from richer countries. This paper contributes widely to the knowledge of health of migrants. Contrary to other evidence, health of women migrants from poorer countries tends to improve with length of stay.