Abstract. Flexibility and dynamics are important for protein function and a protein's ability to accommodate amino acid substitutions. However, when computational protein design algorithms search over protein structures, the allowed flexibility is often reduced to a relatively small set of discrete side-chain and backbone conformations. While simplifications in scoring functions and protein flexibility are currently necessary to computationally search the vast protein sequence and conformational space, a rigid representation of a protein causes the search to become brittle and miss low-energy structures. Continuous rotamers more closely represent the allowed movement of a side chain within its torsional well and have been successfully incorporated into the protein design framework to design biomedically relevant protein systems. The use of continuous rotamers in protein design enables algorithms to search a larger conformational space than previously possible, but adds additional complexity to the design search. To design large, complex systems with continuous rotamers, new algorithms are needed to increase the efficiency of the search. We present two methods, PartCR and HOT, that greatly increase the speed and efficiency of protein design with continuous rotamers. These methods specifically target the large errors in energetic terms that are used to bound pairwise energies during the design search. By tightening the energy bounds, additional pruning of the conformation space can be achieved, and the number of conformations that must be enumerated to find the global minimum energy conformation is greatly reduced.