A set of parallel replicas of a single simulation can be statistically coupled to closely approximate long trajectories. In many cases, this produces nearly linear speedup over a single simulation ( M times faster with M simulations), rendering previously intractable problems within reach of large computer clusters. Interestingly, by varying the coupling of the parallel simulations, it is possible in some systems to obtain greater than linear speedup. The methods are generalizable to any search algorithm with long residence times in intermediate states.