This paper proposes a novel distributed reduced--rank scheme and an adaptive algorithm for distributed estimation in wireless sensor networks. The proposed distributed scheme is based on a transformation that performs dimensionality reduction at each agent of the network followed by a reduced-dimension parameter vector. A distributed reduced-rank joint iterative estimation algorithm is developed, which has the ability to achieve significantly reduced communication overhead and improved performance when compared with existing techniques. Simulation results illustrate the advantages of the proposed strategy in terms of convergence rate and mean square error performance.