  We consider ideals of minors of a matrix, ideals of minors of a symmetric
matrix, and ideals of Pfaffians of an alternating matrix. Assuming these ideals
are of generic height, we characterize the condition $G_{s}$ for these ideals
in terms of the heights of other ideals of minors or Pfaffians of the same
matrix. We additionally obtain bounds on the generation and concentration
degrees of the Rees rings of a subclass of such ideals via specialization of
the Rees rings in the generic case. We do this by proving, given sufficient
height conditions on ideals of minors or Pfaffians of the matrix, the
specialization of a resolution of the Rees ring in the generic case is an
approximate resolution of the Rees ring in question. We end the paper by giving
some explicit generation and concentration degree bounds.
