This paper proposes an activity-specific 3D human pose tracking system from multiple camera views. Dimensionality reduction is used to represent a single activity in a hierarchy of low dimensional spaces. This hierarchy provides increasing independence between limbs by decoupling them, allowing higher flexibility and adaptability that result in improved accuracy. For every subspace, a deterministic optimisation method is applied to estimate the position of the corresponding body parts. Searching through the hierarchy is controlled by an observation function to minimise the computational cost. Evaluation on HumanEva sequences demonstrates that the proposed framework is state-of-the-art both in terms of accuracy and computational complexity.