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Adding a small amount of Al to the well-known high entropy alloy (HEA), Al_0.1CoCrFeNi, to form Al_0.3CoCrFeNi, leads to the precipitation of highly refined ordered L1₂ precipitates, which are stable at 550 °C. However, the L1₂ precipitates (stoichiometry of (Ni,Cr)₃(Al,Fe,Co)) are de-stabilized and replaced by coarser B₂ precipitates on annealing at 700 °C. Contrastingly, in the Co-free, Al_0.3CuCrFeNi₂ high entropy alloy, the L1₂ precipitates are stable at both 550 °C (~ 5 nm) and 700 °C (~ 50 nm), and exhibit a stoichiometry of (Ni,Cu)₃(Al,Fe,Cr). These results lead to interesting insights into the stability of ordered phases in HEAs as a function of composition and temperature.