This paper presents a novel adaptive reduced-rank multi-input-multi-output (MIMO) decision feedback equalization structure based on joint iterative optimization of adaptive estimators. The novel reduced-rank equalization structure consists of a joint iterative optimization of two equalization stages, namely, a projection matrix that performs dimensionality reduction and a reduced-rank estimator that retrieves the desired transmitted symbol. The proposed reduced-rank structure is followed by a decision feedback scheme that is responsible for cancelling the inter-antenna interference caused by the associated data streams. We describe least squares (LS) expressions for the design of the projection matrix and the reduced-rank estimator along with computationally efficient recursive least squares (RLS) adaptive estimation algorithms. Simulations for a MIMO equalization application show that the proposed scheme outperforms the state-of-the-art reduced-rank and the conventional estimation algorithms at about the same complexity.