In the partial relaxation approach, at each desired direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. By adopting this approach, in this paper, a new estimator based on the unconstrained covariance fitting problem is proposed. To obtain the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied. Simulation results show that the performance of the proposed estimator is superior to the classical and other partial relaxation methods, especially in the case of low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a reasonable computational cost.