Our approach to protein–protein docking includes three main steps. First we run PIPER, a new rigid body docking program. PIPER is based on the Fast Fourier Transform (FFT) correlation approach that has been extended to use pairwise interactions potentials, thereby substantially increasing the number of near-native structures generated. The interaction potential is also new, based on the DARS (Decoys As the Reference State) principle. In the second step, the 1000 best energy conformations are clustered, and the 30 largest clusters are retained for refinement. Third, the conformations are refined by a new medium-range optimization method SDU (Semi-Definite programming based Underestimation). SDU has been developed to locate global minima within regions of the conformational space in which the energy function is funnel-like. The method constructs a convex quadratic underestimator function based on a set of local energy minima, and uses this function to guide future sampling. The combined method performed reliably without the direct use of biological information in most CAPRI problems that did not require homology modeling, providing acceptable predictions for targets 21, and medium quality predictions for targets 25 and 26. Proteins 2007. © 2007 Wiley-Liss, Inc.