I don't think your situation is really what some would call low income, but I know someone in a somewhat similar situation. Go to a local small bank, possibly a Credit Union where they keep the mortgage loans in house. They usually underwrite their own mortgages since they don't sell them and are more willing to listen to your actual situation instead of just your debt to income ratio and taxes. Good Luck and hopefully this helps in CA, I am in KY, so not sure what banks can do out there for you. You might also look into renting with your wife and not worry about buying for a while after your PHD program.