Terminal sliding modes (TSM) and their variants have been applied in diverse systems, most notably robotic manipulators. The primary motivations for their application are that they allow for fast and finite-time convergence of the states being controlled to their desired values. In this paper, the design of TSM controllers is considered when the available control magnitude is bounded. In such conditions, it will be shown, by estimating the domain of stability in the system state-space, that not all initial conditions permit the occurrence of terminal sliding mode. Using this method, design guidelines are provided for the selection of the TSM parameters that can allow larger deviations to be handled, when the control is bounded.