Abstract: A compliant engagement member for use with tree-shaking apparatus that resists deformation along the axis of vibration, thereby avoiding dissipation of vibrational energy, yet allows sufficient off-axis deformation to prevent slippage and consequent abrasion of the tree. The engagement member includes a pouch for containing a variable amount of a liquid lubricant; means for conducting a liquid lubricant to and from the pouch; and means for flexibly coupling the pouch to the tree-shaking apparatus. The invention preferably also includes a blanket surrounding at least part of the pouch and frictionally engaging both the pouch and the tree, adding further resistance to slippage against (and consequent injury to) the tree. Lateral inward movement of the shaking device compresses the lubricant pouch against the interior of the contact blanket. The pouch either releases lubricant or is packed sufficiently tightly with lubricant to resist deformation as a result of this compression.