Level of Scrutiny the Supreme Court uses in Freedom of the Press Cases?

I have read the big cases from NY Times v Sullivan 1965 to Hazelwood v Kuhlmeier 1988 and I still can not figure out what level of Scrutiny the Court is usingLevel of Scrutiny the Supreme Court uses in Freedom of the Press Cases?
It would be strict scrutiny





';Strict scrutiny 鈥?To withstand strict scrutiny, a law must be in furtherance of a compelling government interest and go no further than necessary in impeding First Amendment rights. This rigorous test is only applied when there is a substantial interference with First Amendment rights.';