Ship stats

Ogedei-class Liner: Dangerous +5, Dreaded +2, Zailing Speed +75

Il-Altun-class Yacht: Persuasive +5, Respectable +1, Zailing Speed +55, Luxurious +1

Obstinate-class Cruiser: Dangerous +5, Dreaded +5, Zailing Speed +55, greatly reduces Troubled Waters build-up

Nyx-class Zubmersible: Shadowy +5, Dreaded +2, Zailing Speed +55, Zumbersibility +1

All cost 500 Thalassic Favour. No, you can't have several - only one at a time.

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Note: "greatly reduces Troubled Waters build-up" might be an overstatement, since I got up to TW7 several times per trip to Khan's Heart and back when I wasn't careful.

But Obstinate (and the Troubled Waters hat) feel like they make TW management easier, so I guess it works. Not sure about the exact percentage by which it reduces TW, though - didn't measure that one.