A system comprising: a winch system (221; 514; 2106) for an aerial vehicle, wherein the winch system comprises: (a) a tether disposed on a spool, (b) a motor (184, 222, 512) that is operable to apply torque to the tether, and (c) a payload coupling apparatus coupled to a leading end of the tether and structured to mechanically couple a payload to the tether; at least one sensor arranged to generate sensor data indicative of oscillations of the payload coupling apparatus when the tether is at least partially unwound; and a control system operable to, while the aerial vehicle is in a hover flight mode: detect oscillations of the payload coupling apparatus based at least in part on the sensor data; determine that the detected oscillations exceed a threshold; and responsive to determining that the detected oscillations exceed the threshold, perform a damping routine to dampen oscillations of the payload coupling apparatus, characterized in that the damping routine comprises, while the aerial vehicle is in a position-hold mode in which the aerial vehicle substantially maintains a physical position during hover flight by engaging in flight stabilization along three dimensions in physical space, causing the aerial vehicle to reduce an extent of flight stabilization along at least one of the three dimensions, thereby resulting in damping of the oscillations due to energy dissipation during movement of the aerial vehicle along the at least one dimension. a winch system (221; 514; 2106) for an aerial vehicle, wherein the winch system comprises: (a) a tether disposed on a spool, (b) a motor (184, 222, 512) that is operable to apply torque to the tether, and (c) a payload coupling apparatus coupled to a leading end of the tether and structured to mechanically couple a payload to the tether; at least one sensor arranged to generate sensor data indicative of oscillations of the payload coupling apparatus when the tether is at least partially unwound; and a control system operable to, while the aerial vehicle is in a hover flight mode: detect oscillations of the payload coupling apparatus based at least in part on the sensor data; determine that the detected oscillations exceed a threshold; and responsive to determining that the detected oscillations exceed the threshold, perform a damping routine to dampen oscillations of the payload coupling apparatus, characterized in that the damping routine comprises, while the aerial vehicle is in a position-hold mode in which the aerial vehicle substantially maintains a physical position during hover flight by engaging in flight stabilization along three dimensions in physical space, causing the aerial vehicle to reduce an extent of flight stabilization along at least one of the three dimensions, thereby resulting in damping of the oscillations due to energy dissipation during movement of the aerial vehicle along the at least one dimension. detect oscillations of the payload coupling apparatus based at least in part on the sensor data; determine that the detected oscillations exceed a threshold; and responsive to determining that the detected oscillations exceed the threshold, perform a damping routine to dampen oscillations of the payload coupling apparatus, characterized in that the damping routine comprises, while the aerial vehicle is in a position-hold mode in which the aerial vehicle substantially maintains a physical position during hover flight by engaging in flight stabilization along three dimensions in physical space, causing the aerial vehicle to reduce an extent of flight stabilization along at least one of the three dimensions, thereby resulting in damping of the oscillations due to energy dissipation during movement of the aerial vehicle along the at least one dimension.