A variety of different crucible materials have been suggested and/or employed for the sublimation-recondensation growth of AlN single crystals above 2000 C. Representative materials all have melting points well above 2300 C, a reasonable degree of chemical compatibility with AlN, relatively low vapor pressures, and relatively small thermal expansion coefficients. We analyze the current state of knowledge on crucible materials such as C, W, Re, W-Re alloys, BN, HfN, HfC, NbC, TaC, Ta2C, TaN, ZrC and ZrN with respect to published bulk AlN growth conditions. Crucible materials pyrolytic graphite, pyrolytic BN, and W have integrated thermal contraction values (upon cooling from growth temperatures) that are less than that of AlN; the other materials have larger values. The lowest vapor pressure materials in a nitrogen atmosphere are W, TaC, and Re; thus they are expected to yield higher purity crystals than the other candidates. The materials C, BN, Hf, and ZrN are expected to contribute to higher impurity levels in the AlN crystals.