In this article, Adriana Collado summarizes the distinction between parody and satire and the interpretation of this difference in fair use cases over time. Collado goes on to discuss the present state of the law, what the law should be, and possible solutions and compromises for satire, which is not currently mostly included under fair use provisions.
However, Collado also argues that by Supreme Court's own definition of fair use works ("for purposes such as criticism [and] comment"), satire should already been included. Satire has been defined as a commentary or critical work, one of the uses specifically enumerated in the Fair Use Doctrine, so it should technically be protected.
Since satire is currently not included under fair use, Collado discusses potential solutions and compromises, although none are very promising. Collado quotes Tom W. Bell, who suggests that copyright owners and secondary users should be able to opt out of copyright law and contract under a fared use system, although he fails to mention what would happen for satirists if copyright owners refuse to license (which would probably happen due to the self-esteem issue). Collado adds another possibility of courts requiring unauthorized satirists to pay copyright holders for actual damages sustained from the use of the copyrighted work, but understands that such a method might still dissuade satirists who cannot predict such a number in advance.