In this paper we propose two iterative algorithms for the blind separation of convolutive mixtures of sparse signals. The first one, called Iterative Sparse Blind Separation (ISBS), minimizes a sparsity cost function using an approximate Newton technique. The second algorithm, referred to as Givens-based Sparse Blind Separation (GSBS) computes the separation matrix as a product of a whitening matrix and a unitary matrix estimated, via a Jacobi-like process, as the product of Givens rotations which minimize the sparsity cost function. The two sparsity based algorithms show significantly improved performance with respect to the time coherence based SOBI algorithm as illustrated by the simulation results and comparative study provided at the end of the paper.