Loglinear modeling methods have become quite straightforward to apply to discrete data X. A good-fitting loglinear model can be used to generate synthetic copies of X1 ,... , Xn of X that preserve analytic properties but may allow re-identification of small cells. With fitting algorithms that use more general convex constraints and are designed to deal with missing data, we are able to disperse the counts associated with small cells over other cells in a manner that reduces re-identification risk while still maintaining most analytic properties.