This paper proposes the use of the ratio of wavelet extrema numbers taken from the horizontal and vertical counts respectively as a texture feature, which is called aspect ratio of extrema number (AREN). We formulate the classification problem upon natural and synthesized texture images as an optimization problem and develop a coevolving approach to select both scalar wavelet and multiwavelet feature spaces of greater discriminatory power. Sequential searches and genetic algorithms (GAs) are comparatively investigated. The experiments using wavelet packet decompositions with the innovative packet-tree selection scheme ascertain that the classification accuracy of coevolutionary genetic algorithms (CGAs) is acceptable enough.