This paper deals with direction estimation of signals impinging on a uniform linear sensor array. A well-known algorithm for this problem is IQML. However, estimates computed with IQML 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 (WSF-E) with an estimation error covariance which is asymptotically identical to the asymptotic Cramér–Rao lower bound is presented. The WSF-E algorithm resembles weighted subspace fitting (WSF) or MODE, but achieves optimal performance without having to compute an eigendecomposition of the sample covariance matrix.