We present a combination of analytical and experimental results that shed some light into the shape of the cost function of the strategy spaces that query optimizers must deal with. These are the space that includes only left-deep trees and the space that includes both deep and bushy trees. We conclude that the cost functions of both spaces essentially form a “well” but of a distinctly different quality. Based on this result, we discuss how Iterative Improvement, Simulated Annealing, and Two Phase Optimization perform on these spaces. We conclude that the space of both deep and bushy trees is easier to optimize than the space of left-deep trees alone.