A major difficulty for 3D human body tracking from monocular image sequences is the near non-observability of kinematic degrees of freedom that generate motion in depth. For known link (body seg-ment) lengths, the strict non-observabilities reduce to twofold ?for-wards/ backwards flipping? ambiguities for each link. These imply 2^{# links} formal inverse kinematics solutions for the full model, and hence linked groups of O(2^{# links}) local minima in the model-image matching cost function. Choosing the wrong minimum leads to rapid mistracking, so for reliable tracking, rapid methods of inestigating alternative minima within a group are needed. Previous approaches to this have used generic search methods that do not exploit the specific problem structure. Here, we complement these by using simple kinematic reasoning to enumerate the tree of possible forwards/backwards flips, thus greatly speeding the search within each linked group of minima. Our methods can be used either deterministically, or within stochastic ?jump-diffusion? style search processes. We give experimental results on some challenging monocular human tracking sequences, showing how the new kinematic-flipping based sampling method improves and complements existing ones.