In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing behavior is preserved when X is replaced with V Λ X for V finite. In the second part, we introduce chromatic phantom maps. A map is n -phantom if it is null when restricted to finite spectra of type at least n . We define divisibility and finite type conditions which are suitable for studying n -phantom maps. We show that the duality functor W n -1 defined by Mahowald and Rezk is the analog of Brown-Comenetz duality for chromatic phantom maps, and give conditions under which the natural map Y → W 2 n -1 Y is an isomorphism.