This paper presents a time-domain passivity controller for multi-DoF haptic-enabled teleoperation systems aimed at improving performance in terms of transparency for a given task. By solving an online convex optimization problem, the proposed approach enhances transparency of interaction along specific directions of the environment space which are significant for the task at hand, while guaranteeing system stability. An experimental evaluation of the effectiveness of the proposed design is presented, enrolling twenty participants. We compared the performance of the proposed approach vs. those of a standard energy-bounding time-domain algorithm during the exploration of a virtual sphere. Results show that, as the communication delay between the local and remote agents grows, the proposed technique better preserves transparency along the directions that are more important for the task at hand.