Wavelet transform is both sensitive to translation and rotation. This feature of the transform diminishes the discriminative power of wavelet coefficients among different classes where rotated versions of textures are present. We analyze statistical behavior of wavelet coefficients and show that some features of wavelets are more robust than others against translation and rotation. We also show that using higher order moments increase the overall performance. A new parameter is also proposed to determine the discriminative features out of a possible feature set. This new parameter is derived based on statistics of wavelet transform and called as effective discriminative power (EP). Based on EP, reduced subband feature set is proposed and applied on the modified Brodatz database for texture retrieval and shown that the reduced feature set have superior performance compared to the one which just includes mean and standard deviations of all the subbands. The reduced feature set is also computationally less expensive since it eliminates rotation-variant features and results in less number of features with better performance.