What is the ruling on covering women's feet in the Shafi'i school of thought?

According to the Shafi'is, the feet of a free woman have two situations: The first is during prayer, where they are considered 'awrah (Praiseworthy, or in the relied upon and well-known opinion), though some say they are not 'awrah. The second is in front of non-mahram men, where they are 'awrah without dispute and must be covered.