Recent improvements in the protein-structure prediction method developed in our laboratory, based on the thermodynamic hypothesis, are described. The conformational space is searched extensively at the united-residue level by using our physics-based UNRES energy function and the conformational space annealing method of global optimization. The lowest-energy coarse-grained structures are then converted to an all-atom representation and energy-minimized with the ECEPP/3 force field. The procedure was assessed in two recent blind tests of protein-structure prediction. During the first blind test, we predicted large fragments of alpha and alpha+beta proteins [60-70 residues with C(alpha) rms deviation (rmsd) <6 A]. However, for alpha+beta proteins, significant topological errors occurred despite low rmsd values. In the second exercise, we predicted whole structures of five proteins (two alpha and three alpha+beta, with sizes of 53-235 residues) with remarkably good accuracy. In particular, for the genomic target TM0487 (a 102-residue alpha+beta protein from Thermotoga maritima), we predicted the complete, topologically correct structure with 7.3-A C(alpha) rmsd. So far this protein is the largest alpha+beta protein predicted based solely on the amino acid sequence and a physics-based potential-energy function and search procedure. For target T0198, a phosphate transport system regulator PhoU from T. maritima (a 235-residue mainly alpha-helical protein), we predicted the topology of the whole six-helix bundle correctly within 8 A rmsd, except the 32 C-terminal residues, most of which form a beta-hairpin. These and other examples described in this work demonstrate significant progress in physics-based protein-structure prediction.