This paper addresses a major weakness of traditional heart-rate-variability (HRV) analysis for the purpose of monitoring stress: sensitivity to respiratory influences. To address this issue, a linear system-identification model of the cardiorespiratory system using commercial heart rate monitors and respiratory sensors was constructed. Subtraction of respiratory driven fluctuations in heart rate leads to a residual signal where the effects of mental stress become more salient. We experimentally validated the effectiveness of this method on a binary discrimination problem with two conditions: mental stress of subjects performing cognitive tasks and a relaxation condition. In the process, we also propose a normalization method that can be used to compensate for ventilation differences between paced and spontaneous breathing. Our results suggest that, by separating respiration influences, the residual HRV has more discrimination power than traditional HRV analysis for the purpose of monitoring mental stress/load.