In their article "Heads in Oceanic Indirect Possession," published in this journal in 2007, Palmer and Brown make two main claims. First, they argue that the elements that have been analyzed in the recent literature as possessive classifiers are, in at least some Oceanic languages, directly possessed nouns. And second, they argue that these nouns are the heads of indirect possessive constructions. The present study critically reviews their evidence and concludes that (i) there is evidence against analyzing those elements as nouns; and (ii) there is no convincing evidence that those elements are heads. The elements in question form a category of their own, for which the designation "possessive classifiers" is appropriate.