Devices and methods are disclosed for stabilizing tissue within a patient's body during a surgical operation to provide a relatively motionless surgical field. The devices involve tissue stabilizers which provide superior engagement with a tissue structure to be stabilized, for example the beating heart. The tissue stabilizer may have one or more stabilizer feet which provide for adjustment of the orientation of the features which engage the surface of the tissue structure. In one instance, the orientation may be adjusted to ensure the engaging features will be properly aligned with the surface of the tissue structure before engagement. In addition, once engaged with or connected to the tissue structure the orientation may be adjusted to yield an optimum surgical presentation of a portion of the tissue structure, for instance a coronary artery or the like. The tissue stabilizer may be configured to use friction, negative pressure, or both to engage the surface of the heart.