Simulating sample correlation matrices is important in many areas of
statistics. Approaches such as generating normal data and finding their sample
correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise
correlations both have drawbacks. We develop an algorithm for adding noise, in
a highly controlled manner, to general correlation matrices. In many instances,
our method yields results which are superior to those obtained by simply
simulating normal data. Moreover, we demonstrate how our general algorithm can
be tailored to a number of different correlation models.