Metric reconstruction of a scene viewed by an uncalibrated camera undergoing an unknown motion is a fundamental task in computer vision. To obtain accurate results all the methods rely on bundle adjustment, a nonlinear optimization technique which minimizes the reprojection error over the structural and camera parameters. Bundle adjustment is optimal for normally distributed measurement noise, however, its performance depends on the starting point. The initial solution is usually obtained by solving a linearized constraint through a total least squares procedure, which yields a biased estimate. We present a more balanced approach where in main computational modules of an uncalibrated reconstruction system, the initial solution is obtained from a statistically justified estimator which assures its unbiasedness. Since the quality of the new initial solution is already comparable with that of the result of bundle adjustment, the burden on the latter is drastically reduced while its reliability is significantly increased. The performance of our system was assessed for both synthetic data and standard image sequences.