Adjust the H-1B educational eligibility requirement, not the yearly cap.
FY 2012, H-1B data, eliminating bachelors degree eligibility would free up 50% of new H-1B visas.
Data presented by Dr. Ron Hira, shows that legitimate US employers draw heavily from the postgraduate population, while offshore outsourcing firms favor undergraduate degrees. Additionally, the offshore outsourcing firms have the unlimited Intra-company L-1 visa available to them, once the candidate has one year of experience with the firm.
By raising the H-1B educational requirement, citizen and permanent resident candidates would have a better chance at bachelors degree and associate degree level positions, which are the targeted positions to be moved offshore by the offshore outsourcing firms. Restated, 50% more H-1B visas would be available to legitimate US employers.
Institute of International Education, there were 311,204 foreign students enrolled in postgraduate programs in the United States in 2012-13. This might seem like a large number until we factor in the Doctoral programs are four years, and masters and professional degree probably average two years. So the number likely to graduate in 2013 was roughly 126,157 for all declared and undeclared majors (not just STEM). Additionally, some students may not want to stay in the US and other might not graduate, but the 126,157 number is still less than the total number of H-1B initial employment approvals in FY 2012 (136,890),
Work experience authorizations
H-1B lottery and oversubscription
Gaming the number of applications
The ability to apply for hundreds of H-1B visas, on a single application, with the knowledge that application fees will be refunded encourages these companies to oversubscribe the visa category, hoping that their consultant (possibly the same candidate) will be placed at the firms who could not attain the visa at a higher premium. (I.e., if Microsoft doesn't win the lottery on a single LCA, the outsourcing firm, with the un-named H-1B LCAs, can provide the candidate as a consultant.)