  We show that r-mode instabilities severely constraint the composition of a
compact star rotating at a submillisecond period. In particular, the only
viable astrophysical scenario for such an object, present inside the Low Mass
X-ray Binary associated with the x-ray transient XTE J1739-285, is that it has
a strangeness content. Since previous analysis indicate that hyperonic stars or
stars containing a kaon condensate are not good candidates, the only remaining
possibility is that such an object is either a strange quark star or a hybrid
quark-hadron star. We also discuss under which conditions sub-millisecond
pulsars are rare.
