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This paper proposes a novel adaptive reduced-rank filtering scheme based on the joint iterative optimization of adaptive filters. The proposed scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that constitutes the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe minimum mean-squared error (MMSE) expressions for the design of the projection matrix and the reduced-rank filter and simple least-mean squares (LMS) adaptive algorithms for its computationally efficient implementation. Simulation results for a CDMA interference suppression application reveals that the proposed scheme significantly outperforms the state-of-the-art reduced- rank schemes, while requiring a significantly lower computational complexity.