In this paper, the partial relaxation approach is introduced and applied to the direction-of-arrival estimation problem using spectral search. Unlike existing spectral-based methods such as conventional beamformer, Capon beamformer, or MUSIC that can be considered as single source approximation of multisource estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered 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. Thanks to this relaxation, the conventional multi-source optimization problem reduces to a simple spectral search. Following this principle, we propose estimators based on the deterministic maximum likelihood, weighted subspace fitting, and covariance fitting methods. To calculate the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that, irrespective of any specific structure of the sensor array, the performance of the proposed estimators is superior to the conventionalmethods, especially in the case of low signal-to-noise-ratio and low number of snapshots, while maintaining a computational cost that is comparable to MUSIC.