Atomic-accuracy structure prediction of macromolecules should be achievable by optimizing a physically realistic energy function but is presently precluded by incomplete sampling of a biopolymer’s many degrees of freedom. We present herein a working hypothesis, called the “stepwise ansatz,” for recursively constructing well-packed atomic-detail models in small steps, enumerating several million conformations for each monomer, and covering all build-up paths. By making use of high-performance computing and the Rosetta framework, we provide first tests of this hypothesis on a benchmark of 15 RNA loop-modeling problems drawn from riboswitches, ribozymes, and the ribosome, including 10 cases that are not solvable by current knowledge-based modeling approaches. For each loop problem, this deterministic stepwise assembly method either reaches atomic accuracy or exposes flaws in Rosetta’s all-atom energy function, indicating the resolution of the conformational sampling bottleneck. As a further rigorous test, we have carried out a blind all-atom prediction for a noncanonical RNA motif, the C7.2 tetraloop/receptor, and validated this model through nucleotide-resolution chemical mapping experiments. Stepwise assembly is an enumerative, ab initio build-up method that systematically outperforms existing Monte Carlo and knowledge-based methods for 3D structure prediction.