Hybridization of DNA strands can be used to build molecular devices, and control of the kinetics of DNA hybridization is a crucial element in the design and construction of functional and autonomous devices. Toehold-mediated strand displacement has proved to be a powerful mechanism that allows programmable control of DNA hybridization. So far, attempts to control hybridization kinetics have mainly focused on the length and binding strength of toehold sequences. Here we show that insertion of a spacer between the toehold and displacement domains provides additional control: modulation of the nature and length of the spacer can be used to control strand-displacement rates over at least 3 orders of magnitude. We apply this mechanism to operate displacement reactions in potentially useful kinetic regimes: the kinetic proofreading and concentration-robust regimes.