Power: Reading "To the Depths" is not a requirement, but it is recommended.
I wrote this story as an AU AWE sub(ish)-plot. How I can write an AU AWE sub-plot without seeing the movie beforehand defies explanation, but I wanted to go ahead with it anyway.
1) Because this is unlikely to be used in the movie. If it is, I will be very freaked out.
2) Because Weatherby Swann is a stronger character than he's given credit for. So I wanted to write something to show it.

Chapter 1: The Deal

Lord Cutler Beckett stared across the harbour of Port Royal from the balcony of his office. The Flying Dutchman was anchored a little way off shore, longboats bustling back and forth ferrying goods from and crewmen to the harbour. In a short while, the Dutchman would be ready to set sail, under the command of James Norrington.
His attention was drawn away from the sight by a knock on the door. "Enter."
It was Mercer. "Governor Swann would like to see you."
"Send him in."
He disappeared briefly and re-entered with Swann in tow.
"How can I help you, Governor Swann?"
"I came here to ask you if I could request an audience with our newest visitor."
Beckett frowned, exchanging a confused look with Mercer. "Davy Jones? What do you want with him?"
"I was thinking it would be a good idea if I were to formally welcome him to Port Royal. Considering as welcoming notable guests is one of my official duties as Governor, don't you agree that it would be. . . beneficial for the residents to see me acting as I would normally?"
Beckett conceded the point with a nod. Swann had never struck him as a 'brave' man and certainly, deliberately seeking the company of Davy Jones was something that required courage. Perhaps it was just Swann's overpowering curiosity that was getting the better of him. He pondered the request and decided that he could not see the harm in letting the two talk. Perhaps seeing Jones in the flesh would scare Swann into being more compliant. "I do agree. Very well, permission granted."
Swann beamed. "Excellent. You wouldn't happen to know if he likes red wine?"

Weatherby Swann stared out across the bay to where the Dutchman was currently anchored, a bottle of Scottish whiskey clutched in one hand. He had a sent one of the longboats back to notify Jones of his intentions and was waiting for its arrival. It was not long in returning. The crewman who had identified himself as Koleniko informed him that Jones was agreeable to an official welcome, and was to come across in the longboat if it was not too much trouble.
Swann stared down at Koleniko and the longboat, discomforted by the prospect of getting into it, for it had clearly been underwater a lot, and by the prospect of sharing space with the cursed crewman. But he did not have much choice in the matter, so he got in.
The hand that Koleniko offered to help him down into the boat was deathly cold, wet and above all, slimy. He suppressed a shudder and sat down. Something squelched beneath him and it was too his credit that he did not yelp and shoot back up again.
Koleniko, oblivious to the Governor's discomfort, pushed away from the jetty and began to row out to the Dutchman.

The legendary ship was every bit as imposing as the stories had made it out to be and then some. Weatherby Swann swallowed. Suddenly this seemed a bad idea. A ladder was thrown down to him. As was to be expected with everything Dutchman-related, it sported numerous sea life. Swann sighed and ascended the ladder as best he could with one free hand.
Another crewman was waiting for him. This was one was turning into a hammerhead shark. Swann guessed, as he took the proffered lobster-leg-like-fingered hand, that was not the Captain, but equally not a simple deckhand and decided that this was likely to be Jones' First Mate.
"Thank you. Am I correct in assuming you're the First Mate?"
The shark-man looked surprised. "Good guess."
"And where is Captain Jones, pray tell?"
"Waiting for you. Follow me."
"You didn't tell me your name."
The First Mate held out his other, more human hand, grinning toothily. "First Mate of the Flying Dutchman, Mr. Maccus."
Swann smiled back and shook hands. "A pleasure to make your acquaintance, Mr. Maccus."
He was lead to the helm where Davy Jones was sitting before a table that had clearly been thrown together.
"I'm aware that this is not to your usual standards, Governor, but I hope it will suffice," Jones drawled in his Scottish accent.
Governor Swann nodded and smiled, feeling slighted by the fact that Jones had not got to his feet to greet him.
The Captain gestured to the chair opposite him. "Please take a seat. I asked for it especially." Evidently he had also asked for one for himself as well.
That was something at least. Jones had not completely forgotten common courtesy. He sat down at the makeshift table and placed the bottle down on it for Jones to see. Swann smiled when he saw the Scotsman's eyes light up.
"Dare I ask. . . ? Is that Scottish whiskey?"
"It is. I wasn't able to procure the name of your favourite brand, unfortunately. Will that do?"
"It certainly will," he replied picking the bottle up to inspect it. "Mr. Maccus, I believe we have some tankards in the hold."
"Aye, Captain."
"Oh, I won't have any, thank you," Swann said, hastily.
"One for me, then. And get one for yourself."
Maccus beamed and stepped to it.
Jones placed the bottle back on the table and lent back in his chair, regarding the Governor with ice-blue eyes. "Now tell me, Governor, what has compelled you to seek out an audience with me?"
Swann stared back innocently. "What do you mean?"
"I know you have an ulterior motive. A man such as yourself would not come out here to seek an audience with the feared Davy Jones, just to say "Hello"."
Weatherby sighed. "Am I really that obvious?"
"About as obvious as uttering the summoning rhyme."
That alarmed him. "Does this mean that Beckett knows?"
Jones scoffed. "I doubt it. I've been around longer than the pair of you put together. I've seen all kinds of men willing to make deals for this, that, and the other. As such, I can tell when someone comes to me with the intention of striking a deal."
Maccus reappeared with two tankards in hand.
"Good timing, Maccus. Our friend here was just about to reveal his hidden agenda."
"Oh good. I haven't missed anything," he replied pouring himself and Jones some whiskey.
"You were saying, Governor."
"My offer is to reunite you with your heart and ultimately your freedom."
Without meaning too, he had timed that revelation to catch the pair in mid-swallow of a swig of whiskey. Maccus spat it out and gaped at him. Jones on the other hand, attempted to utter an exclamation of surprise and swallow whiskey at the same time, but had to settle for choking it down instead. He thumped himself in the chest, coughing, and blinked back tears. "Could you repeat that? I don't think I heard you properly."
So he did.
"In my experience, no-one does anything for nothing, least of myself. What do you want in exchange?"
"My daughter. She's out there somewhere. She left Port Royal in pursuit of her fiancé and they told me that she has got or could get mixed up in some nasty business. Becket promised her safety in exchange for my loyalty to the East India Trading Company. But I don't trust him."
Jones tilted his head to one side. If Bootstrap Bill Turner had been there to council Swann, he would have informed the Governor that this was a positive sign. "And you trust me?"
"You've never gone back on your word," he replied simply.
Jones smiled; good answer. "I'm curious though, you don't seem too concerned about the fate of your future son-in-law."
"I'm sure young William Turner can take-"
"William Turner!?"
Swann blinked, surprised at the hostility in the Captain's tone. "You know him?"
"If we are indeed talking about the same Turner, aye, I know him. Both of them in fact."
"The William Turner I'm referring to went off after Jack Sparrow. I'm sure-"
"Jack Sparrow!?" Apparently the name was as displeasing as William Turner's.
"So we are talking about the same Turner, then."
"Small world, isn't it?" Maccus commented.
Weatherby suddenly had a thought. "If you saw William, did you see Elizabeth? Was she with him?"
Jones lent back in his chair, pondering. He recalled spotting a young woman on the deck of the Black Pearl shortly before the Dutchman attacked. "Aye," he said nodding slowly. "That girl must have been Elizabeth."
"Then she's safe!" He clasped his hands together in a prayer. "Thank heavens."
Jones smirked. "Ah, I can't say that much. I do know that she made it off the Black Pearl before the Kraken dragged it down. But safe?"
Governor Swann looked back at him sharply. "The Black Pearl? Gone?"
"Aye." Jones replied, looking pleased with himself. "Jack Sparrow and the Black Pearl are no more."
"But not Elizabeth? Or William? You're sure of this?"
"Positive. The Kraken told me that she only devoured one, and that was Jack Sparrow."
Swann winced in sympathy. He may not have thought much of the man, but he would not have wished the Kraken on anyone, even Beckett, the man who simply looked like his old friend. . . Well, perhaps Mercer. (A/N 1)
"So how do you plan to retrieve my heart? You won't be able to just walk in, pick it up and leave."
"Actually. . . That was exactly what I was going to do."
Jones stared at him for a minute. "And this is going to work?"
"They won't expect it. Not from me."
He nodded slowly. "Aye. A good point. But I'm still somewhat concerned. My life hangs in the balance if things don't go according to plan."
"And so does the life of my daughter. I can't lose her, Jones. She's all I have left."
A pause. "In that case, Governor Swann, I believe I can trust you."
Weatherby looked up that, into Jones' cold blue eyes, and then down at his outstretched hand.
"We have a deal."
He smiled, relieved and happily shook the Captain's hand, ignoring its squishy, slimy texture and the tentacle that curled around his arm.

A/N 1: The fact that the Kraken is female and can talk doesn't seem to surprise him. XD

Power: This is probably going to span about 3 or 4 chapters and will end on a cliffhanger of sorts. After I watch the movie and get ideas of how far-reaching the consequences of this ficlet are, I will continue to write. Or I could leave it to your imagination. Or I could leave it for someone else to write. XD We'll see.
Anyway, I hope you enjoy this little outing from me.