A fundamental fact is that any quantization of the bialgebra of functions on a reductive group is equivalent to a "preferred deformation" -- one in which the comultiplication is strictly unchanged on all elements. This is true, in particular, for the standard quantizations of SL(n). However, the explicit form of the preferred deformation is unknown in all cases, even for SL(2). I will review the status of this problem in the case of SL(2) and report on some ongoing research which may explicitly yield the preferred deformation.