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In dynamical systems examples are common in waich there are regions containing chaotic sets that are not attractors, eg systems with horseshoes have such regions. In such dynamical systems one will observe chaotic transients. An important problem is the'Dynamical Restraint Problem': given a region that contains a chaotic set but contains no attractor, find a chaotic trajectory numerically that remains in the region for an arbitrarily long period of time. We present two procedures ('PIM triple procedures') for finding trajectories which stay extremely close to such chaotic sets for arbitrarily long periods of time.