Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for recon- struction. In this paper we expand our theory for distributed compressed sensing (DCS) that enables new distributed cod- ing algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS the- ory rests on a new concept that we term the joint sparsity of a signal ensemble. We present a second new model for jointly sparse signals that allows for joint recovery of multi- ple signals from incoherent projections through simultane- ous greedy pursuit algorithms. We also characterize theo- retically and empirically the number of measurements per sensor required for accurate reconstruction.