3D ultrasound imaging has enabled minimally invasive, beating heart intracardiac procedures. However, rapid heart motion poses a serious challenge to the surgeon that is compounded by significant time delays and noise in 3D ultrasound. This paper investigates the concept of using a one-degree-of-freedom motion compensation system to synchronize with tissue motions that may be approximated by 1D motion models. We characterize the motion of the mitral valve annulus and show that it is well approximated by a 1D model. The subsequent development of a motion compensation instrument (MCI) is described, as well as an extended Kalman filter (EKF) that compensates for system delays. The benefits and robustness of motion compensation are tested in user trials under a series of non-ideal tracking conditions. Results indicate that the MCI provides an approximately 50% increase in dexterity and 50% decrease in force when compared with a solid tool, but is sensitive to time delays. We demonstrate that the use of the EKF for delay compensation restores performance, even in situations of high heart rate variability. The resulting system is tested in an in vitro 3D ultrasound-guided servoing task, yielding accurate tracking (1.15 mm root mean square) in the presence of noisy, time-delayed 3D ultrasound measurements.