An unmanned aerial vehicle (UAV) can deliver a package to a delivery destination. Packages delivered by a UAV may be lowered towards the ground while the UAV continues to fly rather than the UAV landing on the ground and releasing the package. Packages may sway during lowering as a result of wind or movement of the UAV. A package sway may be monitored and mitigated by rapidly paying out a tether, when using a winch mechanism, to dissipate the energy of the sway as downward energy. Further, the UAV may navigate in the direction of the sway or reduce the altitude of the UAV to dissipate the energy of the sway. Open-loop and/or closed loop drop techniques may be utilized to lower a package from the UAV, and the package may be released in the air or on the ground.