In previous work [10], we have proposed a new signal representation for audio coding, where the signal is decomposed in a union of MDCT bases using matching pursuit. The resulting coder gave better performance than a transform coder at low bitrates but slightly worse at high bitrates. In this paper, we propose an adaptive matching pursuit algorithm that in the first iterations decomposes the signal into the redundant union of MDCT bases, and then, when the residual energy decay becomes too low, switches to an orthogonal basis (one of the MDCT bases). We investigate simple strategies to determine in which iteration switching is near-optimal in terms of rate-distortion. We present in this paper a prototype audio coder based on this algorithm, that reaches the performance of the previous approach at low bitrates and the one of transform coding at high bit rates.