(Reuters) - U.S. lawmakers are considering proposals to deal with a rising number of U.S. companies reincorporating overseas to slash their tax bills. The U.S. Treasury Department on Monday announced new rules that will reduce the tax benefits to companies that make these inversion deals. But Democratic lawmakers said more could still be done to curb the deals. Here is what lawmakers are considering: WHAT IS AN INVERSION? In an inversion, a U.S. company buys or sets up a foreign company. Then the U.S. company shifts its tax domicile to that foreign company and its home country, making the U.S. operation a subsidiary unit. If the transaction meets U.S. Internal Revenue Service standards, it can allow the former U.S. company to reduce its American corporate taxes by, for instance, making foreign profits no longer subject to U.S. taxation. 50 PERCENT RULE Under IRS rules, for an inverted company to be considered foreign-owned, 20 percent or more of its shareholders must be foreign investors who did not own stock in the old U.S. company. To be considered foreign-owned, but with some restrictions, there is also a 40 percent foreign ownership requirement. Senator Carl Levin and Representative Sander Levin, Michigan Democrats who are brothers, have offered legislation proposing a higher minimum foreign ownership hurdle of 50 percent. President Barack Obama has proposed a similar change. The Levins also propose denying foreign company status to a company whose management remains chiefly in the United States. GOVERNMENT CONTRACTS Carl Levin and Senator Dick Durbin, an Illinois Democrat, have proposed barring government agencies from signing contracts with inverted companies, using Levin's proposed definition that would encompass more companies. Some experts say Obama could take this step on his own. EARNINGS STRIPPING One way inverted companies cut taxes is called earnings stripping. This frequently involves the foreign headquarters lending money to the U.S. unit, which then sends U.S. profits back overseas as interest payments. The payments are tax deductible in the United States and often tax-free abroad. Senator Chuck Schumer, a New York Democrat, has proposed limiting the interest deductions companies can claim. His proposal would apply to deals reached as far back as 1994. Representative Mark Pocan, a Wisconsin Democrat, has also introduced legislation capping deductions. EXIT TAX Often, U.S. companies with substantial foreign earnings will hold cash or invest abroad because those profits are not subject to U.S. taxes unless they are brought into the United States, or repatriated. Senator Sherrod Brown, an Ohio Democrat, and Durbin want to force U.S. companies to pay a one-time "exit" tax on income that has not been repatriated if the companies decide to invert. OTHER POSSIBILITIES While they have generally opposed Democrats' proposals, Republicans have said they want broader tax code reform that would lower corporate rates and move to a territorial system in which U.S. companies pay little or no tax on foreign profits. (Reporting by Emily Stephenson; Editing by Kevin Drawbaugh, Cynthia Osterman, Jonathan Oatis and Leslie Adler)