Abstract We describe four criteria for the selection of alloying elements capable of producing castable, precipitation-strengthened Al alloys with high-temperature stability and strength: these alloying elements must (i) be capable of forming a suitable strengthening phase, (ii) show low solid solubility in Al, (iii) low diffusivity in Al, and (iv) retain the ability for the alloy to be conventionally solidified. With regard to criterion (i), we consider those systems forming Al3M trialuminide compounds with a cubic L12 crystal structure, which are chemically and structurally analogous to Ni3Al in the Ni-based superalloys. Eight elements, clustered in the same region of the periodic table, fulfill criterion (i): the first Group 3 transition metal (Sc), the three Group 4 transition metals (Ti, Zr, Hf) and the four latest lanthanide elements (Er, Tm, Yb, Lu). Based on a review of the existing literature, these elements are assessed in terms of criteria (ii) and (iii), which satisfy the need for a dispersion...