Frege held that indexical thoughts could be retained through changes of context that required a change of indexical term. I argue that Frege was partially right in that a singular mode of presentation can be retained through changes of indexical. There must, however, be a further mode of presentation that changes when the indexical term changes. This suggests that indexicals should be regarded as complex demonstratives; a change of indexical term is like a change between 'that φ' and 'that ψ', (...) where 'φ' and 'ψ' pick out relational properties that may nonetheless be conceived of by the thinker as intrinsic. (shrink)