Embodiments described herein may help to provide medical support via a fleet of unmanned aerial vehicles (UAVs). An illustrative UAV may include a housing, a payload, a line-deployment mechanism coupled to the housing and a line, and a payload-release mechanism that couples the line to the payload, wherein the payload-release mechanism is configured to release the payload from the line. The UAV may further include a control system configured to determine that the UAV is located at or near a delivery location and responsively: operate the line-deployment mechanism according to a variable deployment-rate profile to lower the payload to or near to the ground, determine that the payload is touching or is within a threshold distance from the ground, and responsively operate the payload-release mechanism to release the payload from the line.