We propose a new computational approach for protein docking exploiting energy funnels in the 6-dimensional space of translations and rotations of the ligand with respect to the receptor. Our approach consists of a series of translational and orientational moves of the ligand towards the receptor. Each move is performed using a global optimization method we have developed - the semi-definite underestimation (SDU) method - which can exploit a funnel-like energy function. We compared our approach with Monte Carlo on a set of 10 protein complexes using two residue-level potentials. To achieve the same level of performance (produce a near-native < or =3 A RMSD complex) our approach reduces energy evaluations by more than a factor of two, on average.