Two efficient and complementary sampling algorithms are presented to explore the space of closed clash-free conformations of a flexible protein loop. The "seed sampling" algorithm samples conformations broadly distributed over this space, while the "deformation sampling" algorithm uses these conformations as starting points to explore more finely selected regions of the space. Computational results are shown for loops ranging from 5 to 25 residues. The algorithms are implemented in a toolkit, LoopTK, available at https://simtk.org/home/looptk.