Direct ship-to-ship lightering of large crude oil tankers via small vessels to enable the former to enter shallow channels and ports is an extremely crucial operation in crude transportation. We consider a scheduling problem faced by a shipping company that operates a fleet of multicompartment service vessels with different configurations to provide lightering services for multiple refineries clustered in a region. In contrast to limited existing work on the tanker-lightering problem, we address several realistic and practical problem considerations such as multicompartment vessels, limitation on simultaneous transfers, crude density variations, etc. We develop two continuous-time, slot-based, mixed-integer linear programming (MILP) models using different linearization methods and address two objectives of minimizing tanker demurrage and time-charter costs. The model requiring additional continuous variables but fewer nonzeros and constraints generally performs better. In addition, we develop a simplified model based on some intuitive, albeit heuristic, considerations to enable the solution of real-scale problems. A numerical comparison of our best slot-based model with existing event-based models for simplified versions of our general problem shows that the former is faster.