To accurately predict protein conformations in atomic detail, a computational method must be capable of sampling models sufficiently close to the native structure. All-atom sampling is difficult because of the vast number of possible conformations and extremely rugged energy landscapes. Here, we test three sampling strategies to address these difficulties: conformational diversification, intensification of torsion and omega-angle sampling and parameter annealing. We evaluate these strategies in the context of the robotics-based kinematic closure (KIC) method for local conformational sampling in Rosetta on an established benchmark set of 45 12-residue protein segments without regular secondary structure. We quantify performance as the fraction of sub-Angstrom models generated. While improvements with individual strategies are only modest, the combination of intensification and annealing strategies into a new "next-generation KIC" method yields a four-fold increase over standard KIC in the median percentage of sub-Angstrom models across the dataset. Such improvements enable progress on more difficult problems, as demonstrated on longer segments, several of which could not be accurately remodeled with previous methods. Given its improved sampling capability, next-generation KIC should allow advances in other applications such as local conformational remodeling of multiple segments simultaneously, flexible backbone sequence design, and development of more accurate energy functions.