This paper presents novel adaptive reduced-rank filtering algorithms based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that constitute the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe least squares (LS) expressions for the design of the projection matrix and the reduced-rank filter and recursive least squares (RLS) adaptive algorithms for its computationally efficient implementation. Simulations for a space-time interference suppression in a CDMA system application show that the proposed scheme outperforms in convergence and tracking the state-of-the-art reduced-rank schemes at about the same complexity.