We describe and apply a flexible, adaptive cosine packet transform to separate audio sources from instantaneous, underdetermined audio mixtures by time-frequency masking. Previously studied adaptive transform schemes have two main drawbacks: the signal can only be partitioned into dyadic intervals, and the profiles of the overlapping windows are often very short, thus tapering off very quickly. The novel aspects of our new approach are that it admits a much larger library of admissible orthogonal bases, and thus does not require dyadic segmentation and alleviates border artifacts at window boundaries.