A majority of Americans believe press freedom is important. Far fewer believe the press is actually free.

Though two-thirds of Americans believe press freedom is very important, only a third say that the media is actually completely free to report the news, according to a Pew Research Center study released Thursday.

That gap — where more people say press freedom is important than report actually having it — is found across countries as diverse as Chile and Turkey, the study finds. Pew’s study is based on surveys of more than 50,000 adults across 35 countries and covers perceptions of free speech and internet freedom in addition to press freedom.