This paper introduces an approach to wavelet packet best basis searches using the generalized Renyi entropy. The approach extends work by R.R. Coifman and M.V. Wickerhauser who showed how Shannon entropy can be used as an additive cost function in the wavelet packet best basis selection (see IEEE Trans. on Inform. Theory, vol.38, no.2, p.713-18, 1992). This paper also extends the idea of an additive cost function to an arithmetic mean. These extensions allow for a redefinition of additive cost functions as arithmetic means in a way consistent with the approach of Coifman and Wickerhauser. The approach using an arithmetic mean is then extended to include the geometric mean. This extension to geometric means allows us to introduce the Renyi generalized entropy as a cost function in the best basis search. These two extensions also allow the use of incomplete probability distributions, whereas Coifman and Wickerhauser's entropy based cost function is limited to complete probability distributions.