More than half of Americans believe we should have stricter gun control laws, according to a comprehensive new report by the Pew Research Center, which surveyed nearly 4,000 people this year.

The report highlights Americans’ complicated beliefs and feelings about guns. Beliefs about the causes of gun violence and the need for gun laws are strictly divided between those who actually own guns and and those who do not. The former group generally does not favor stricter gun laws.

There are a few areas of overlap. At least 82 percent of all those surveyed said that gun ownership should be restricted for the mentally ill and for individuals on “no fly” lists. Gun owners and non-gun owners alike also agree that there should be background checks at private sales and gun shows. Known as the “gun show loophole,” guns sold on the secondary market in the U.S. are currently exempt in most states from background checks.

Still, “debates over gun policy remain sharply polarized,” the report concluded.