  Here we show that any n-dimensional centrally symmetric convex body K has an
n-dimensional perturbation T which is convex and centrally symmetric, such that
the isotropic constant of T is universally bounded. T is close to K in the
sense that the Banach-Mazur distance between T and K is O(log n). If K has a
non-trivial type then the distance is universally bounded. In addition, if K is
quasi-convex then there exists a quasi-convex T with a universally bounded
isotropic constant and with a universally bounded distance to K.
