Recent works have shown the superiority of the 2q-MUSIC (q ges 2) approach over the well-known second order MUSlC-like methods, especially when some resolution is needed or when more sources than sensors have to be processed.. In addition, the performance of 2q-MUSIC (q ges 2) increase as q increases, to mention that these higher order (HO) MUSIC-like algorithms are robust to the presence of a strong background noise which spatial coherence is unknown. However, even the 2q-MUSIC (q ges 2) methods have their limitations, for instance, when more resolution is required or when the dimension of the source space increases strongly. Indeed, in such operational contexts, the search of local minima in the 2q-MUSIC metric is a real problem. So, in order to improve the 2q-MUSIC approach, this paper proposes new MUSIC-like algorithms, namely 2q-D-MUSIC (q ges 1) and 2q-RapMUSIC (q ges 2), based on an efficient 2q-th order deflation scheme (DS). The HO deflation procedure increases the estimation resolution at each step taking optimally into account, in the overdetennined case, the presence of possibly but not completely statistically dependent sources. As far as the computational cost is concerned, it is strongly reduced by way of a recursive procedure.