Many proteins contain regions of unstructured polypeptide chain that appear to be flexible and to undergo random thermal motion. In some cases the unfolded sequence acts as a flexible tether that restricts the diffusion of a globular protein domain for the purpose of catalysis or self-assembly. In this article, we present a stochastic model for tethered protein domains under various conditions and solve it numerically to deduce the general and dynamic properties of these systems. A critical domain size dependent on the length of the tether is presented, above which a spherical domain tethered to an impenetrable wall by a flexible chain displays a restricted localization between two concentric half-shells. Results suggest that the diffusion of such a spherical domain is effectively reduced in its dimensionality and able to explore the available space with high efficiency. It also becomes clear that the orientation of the ball is not independent of the distance from the tethering point but becomes more constrained as the linking tether is extended. The possible biological significance of these and other results is discussed.