H-1B visas are designed to bring foreign professionals with college degrees and specialized skills to fill jobs when qualified Americans cannot be found. But in recent years, global outsourcing companies have dominated the program, winning tens of thousands of visas and squeezing out many American companies, including smaller start-ups. Congress set a limit of 85,000 visas annually, and more than 10,000 companies applied in 2014. But just 20 companies received more than 32,000 visas, according to Ronil Hira, a professor at Howard University who studies visa programs and analyzed federal H-1B data. The top 20 included several large outsourcing firms...