A Shell oil-drilling ship that ran aground near a remote Alaska island is under tow again.

The Unified Command for the operation in Anchorage says the Kulluk is being towed at about 5 mph to shelter in Kodiak Island's Kiliuda Bay. Officials won't estimate its arrival because of weather conditions early Monday - winds of about 18 mph and 15-foot ocean swells.

There's a salvage crew of 10 people on board and one Royal Dutch Shell representative.

The Kulluk was refloated late Sunday from rocks. There's no sign of any oil discharge from the vessel. It was being towed to Seattle for maintenance when it ran aground in a powerful storm on New Year's Eve.