We consider the capacity of a single user t /spl rarr/ /spl tau/ MIMO wireless system in a Rayleigh or Ricean fading environment. It is known that a certain central limit theorem exists which states (under certain conditions) that the distribution of the standardized capacity is asymptotically Gaussian as r /spl rarr/ /spl infin/, t /spl rarr/ /spl infin/ and /spl tau//t /spl rarr/ y for some constant y. However we demonstrate the surprising accuracy of a Gaussian approximation to the capacity for virtually all values of /spl tau/ and t. In order to investigate the accuracy of the Gaussian fit we derive the variance of the capacity in the Rayleigh fading case.