Pure random search is undeniably the simplest stochastic search algorithm for numerical optimization. Essentially the only thing to be determined to implement the algorithm is its sampling space, the influence of which on the performance on the bi-objective bbob-biobj test suite of the COCO platform is investigated here. It turns out that the suggested region of interest of [−100, 100] n (with n being the problem dimension) has a too vast volume for the algorithm to approximate the Pareto set effectively. Better performance can be achieved if solutions are sampled uniformly within [−5, 5] n or [−4, 4] n. The latter sampling box corresponds to the smallest hypercube encapsulating all single-objective optima of the 55 constructed bi-objective problems of the bbob-biobj test suite. However, not all best known Pareto set approximations are entirely contained within [−5, 5] n .