This paper presents two novel data assimilation (DA) techniques for reconstructing steady turbulent flows at high Reynolds numbers by introducing perturbations to the Reynolds stress tensor computed by the turbulence model of a Favre-averaged Navier–Stokes (FANS) code. These techniques minimize the least-squares difference between an experimentally measured mean flow quantity and the corresponding quantity as computed by the FANS code. The two DA methods differ from each other in the choice of the control parameters: one perturbs the eigenvalues and eigenvectors of a baseline Reynolds stress, whereas the other perturbs the components of a baseline realizable Reynolds stress such that the perturbed result is still realizable. For the optimization procedure, a gradient-based algorithm is used in combination with a discrete adjoint methodology. The DA methods are applied to high-Reynolds-number problems, and their results compared with a reference technique. The results show that the approaches developed in this work are more effective at reconstructing the turbulent flowfield than standard techniques, but are more computationally expensive due to the high dimensionality of the optimization problem. Furthermore, it appears that only small perturbations to the control parameters are necessary to obtain significant improvements over the baseline results.