In this paper we present a new sparse iterative covariance-based estimation approach, called SPICE, to the direction of arrival estimation problem. SPICE is obtained by the minimization of a statistically well motivated covariance matrix fitting criterion and can be used in both single and multiple-snapshot cases. Some of the unique features enjoyed by SPICE are : it takes account of the noise in the data in a natural manner, it does not require selection of any hyperparameters, and it has global convergence properties.