The area of blind system identification using Higher-Order-Statistics has gained considerable attention over the last two decades. This paper, motivated by the recent developments in sparse approximations, proposes new algorithms for the blind identification and order determination of sparse systems. The methodology used relies on greedy schemes. In particular, the first algorithm exploits a single step greedy structure, while the second improves performance using a threshold-based selection procedure. Finally, the proposed algorithms are tested on a wide range of randomly generated channels and different output signal lengths.