Many search algorithms have parameters that need to be tuned to get the best performance. Typically, the parameters are tuned offline, resulting in a generic setting that is supposed to be effective on all problem instances. For suboptimal single-agent search, problem-instance-specific parameter settings can result in substantially reduced search effort. We consider the use of dovetailing as a way to take advantage of this fact. Dovetailing is a procedure that performs search with multiple parameter settings simultaneously. Dovetailing is shown to improve the search speed of weighted IDA* by several orders of magnitude and to generally enhance the performance of weighted RBFS. This procedure is trivially parallelizable and is shown to be an effective form of parallelization for WA* and BULB. In particular, using WA* with parallel dovetailing yields good speedups in the sliding-tile puzzle domain, and increases the number of problems solved when used in an automated planning system.