In this paper, we respond to Tomberlin's objections. However, we first correct his account of the way in which we would meet one of his challenges for actualism. Tomberlin's second challenge for actualism is this: offer a credible treatment (i.e., an analysis that preserves truth and entailments) of the sentence `Ponce de Leon searched for the fountain of youth' which does not require Ponce de Leon to stand in a de re relation to some non-actual individual. Tomberlin asserts that we would analyze this claim as a relation between Ponce de Leon and a contingently nonconcrete individual. Since our view is that contingently nonconcrete individuals are actual, it would appear that we have met his challenge. However, we would not analyze the claim in question the way Tomberlin suggests. We sharply distinguish between contingently nonconcrete objects, which we proposed for the analysis of modality, and genuine abstract objects, which we think are needed for the analysis of intentional relations. On our view, the objects needed for the analysis of modality are just the wrong kind of thing for the analysis of intentionality. In the body of the paper, therefore, we first explain why we deny the not uncommon view that `possibilia' (or actualist reconstructions thereof) are suitable as intentional objects and afterwards respond to the specific objections that Tomberlin raises against our view.