Iterated doubles of the Joker and their realisability

Let A(1)^* be the subHopf algebra of the mod2 Steenrod algebra A^* generated by Sq^1 and Sq^2. The Joker is the cyclic A(1)^*-module A(1)^*/A(1)^*{Sq^3} which plays a special role in the study of A(1)^*-modules. We discuss realisations of the Joker both as an A^*-module and as the cohomology of a spectrum. We also consider analogous A(n)^*-modules for n=>2 and prove realisability results for n=2,3 and non-realisability results for n=>4.