For single-domain proteins, we examine the completeness of the structures in the current Protein Data Bank (PDB) library for use in full-length model construction of unknown sequences. To address this issue, we employ a comprehensive benchmark set of 1,489 medium-size proteins that cover the PDB at the level of 35% sequence identity and identify templates by structure alignment. With homologous proteins excluded, we can always find similar folds to native with an average rms deviation (RMSD) from native of 2.5 A with approximately 82% alignment coverage. These template structures often contain a significant number of insertions/deletions. The tasser algorithm was applied to build full-length models, where continuous fragments are excised from the top-scoring templates and reassembled under the guide of an optimized force field, which includes consensus restraints taken from the templates and knowledge-based statistical potentials. For almost all targets (except for 2/1,489), the resultant full-length models have an RMSD to native below 6 A (97% of them below 4 A). On average, the RMSD of full-length models is 2.25 A, with aligned regions improved from 2.5 A to 1.88 A, comparable with the accuracy of low-resolution experimental structures. Furthermore, starting from state-of-the-art structural alignments, we demonstrate a methodology that can consistently bring template-based alignments closer to native. These results are highly suggestive that the protein-folding problem can in principle be solved based on the current PDB library by developing efficient fold recognition algorithms that can recover such initial alignments.