The increasing availability of “utility computing” resources such as clouds, grids, and massively parallel shared clusters can provide practically unlimited processing and memory capacity on demand, at some cost per unit of resource usage. This requires a new perspective in the design and evaluation of parallel search algorithms. Previous work in parallel search implicitly assumed ownership of a cluster with a static amount of CPU cores and RAM, and emphasized wallclock runtime. With utility computing resources, trade-offs between performance and monetary costs must be considered. This paper considers dynamically increasing the usage of utility computing resources until a problem is solved. Efficient resource allocation policies are analyzed in comparison with an optimal allocation strategy. We evaluate our iterative allocation strategy by applying it to the HDA* parallel search algorithm. The experimental results validate our theoretical predictions. They show that, in practice, the costs incurred by iterative allocation are reasonably close to an optimal (but a priori unknown) policy, and are significantly better than the worst-case analytical bounds.