We present a method for recovering three-dimensional (3D) human body motion from monocular video sequences based on a robust image matching metric, incorporation of joint limits and non-self-intersection constraints, and a new sample-and-refine search strategy guided by rescaled cost-function covariances. Monocular 3D body tracking is challenging: besides the difficulty of matching an imperfect, highly flexible, self-occluding model to cluttered image features, realistic body models have at least 30 joint parameters subject to highly nonlinear physical constraints, and at least a third of these degrees of freedom are nearly unobservable in any given monocular image. For image matching we use a carefully designed robust cost metric combining robust optical flow, edge energy, and motion boundaries. The nonlinearities and matching ambiguities make the parameter-space cost surface multimodal, ill-conditioned and highly nonlinear, so searching it is difficult. We discuss the limitations of CONDENSATION-like samplers, and describe a novel hybrid search algorithm that combines inflated-covariance-scaled sampling and robust continuous optimization subject to physical constraints and model priors. Our experiments on challenging monocular sequences show that robust cost modeling, joint and self-intersection constraints, and informed sampling are all essential for reliable monocular 3D motion estimation.