This paper deals with direction estimation of signals impinging on a uniform linear sensor array. A well known algorithm for this problem is iterative quadratic maximum likelihood (IQML). Unfortunately, the IQML estimates are in general biased, especially in noisy scenarios. We propose a modification of IQML (MIQML) that gives consistent estimates at approximately the same computational cost. In addition, an algorithm with an estimation error covariance which is asymptotically identical to the asymptotic Cramer-Rao lower bound is presented. The optimal algorithm resembles weighted subspace fitting or MODE, but achieves optimal performance without having to compute an eigendecomposition of the sample covariance matrix.