The fastest way I've found so far is in Mahogany Hall; it requires a very high Persuasive skill. If you train the Louche Devil and teach him Philosophy, you'll get 111 Nevercold Brass Slivers per action and increase your Pygmalion quality. When Pygmalion reaches 17 or 18, you should be safe to take him out to a Society dinner, which gives you 1000 bonus slivers. ... You can then re-train him as often as you like to rack up lots of Echoes.
If you want to do it with your Dangerous, head to the third coil of the Labyrinth of Tigers. "Avoid becoming an exhibit yourself" and "Fight back" for ~1 Echo per action. (Most of the actions in the third coil earn ~1 Echo per action, but they require a very high Persuasive as well.)
Option #1: Oblivion in laudanum.
The solution is extremely Victorian: F.F. Gebrandt's Superior Laudanum, to help you sleep at night. You can find it in the Echo Bazaar (click the "Bazaar" tab), in the shop Nikolas Pawnbrokers. Each bottle costs one Echo, which can be quite pricey if you're trying to sell Whispered Secrets or the like in the Bazaar.
Drinking laudanum is bad for your health, and your Wounds quality will increase a bit one change point), but you can reduce that with F.F. Gebrandt's Tincture of Vigour. I imagine that Gebrandt is an extremely wealthy lady. Alternatively, you can just rest at your Lodgings if your Wounds quality is 3 or higher.
Once you become a Person of Some Importance (PoSI), as with the Tincture of Vigour and Ablution Solution, this option will become less viable; unlike the other two, it will also have a nasty side-affect: every time you drink a bottle of the stuff, you'll become slightly more addicted to it, resulting in the Laudanum becoming less effective.
Option #2: We're all mad here.
Go to A state of some confusion. It will discard and replace all of your Opportunities with new cards, so don't do it if you really like your current Opportunities. Almost all of the Opportunities and actions available in confusion will decrease your Nightmares (though some will abuse your base stats a bit, and one or two will increase your Nightmares while giving you something else you want), and you will leave A state of some confusion once your Nightmares drops to zero.
There are two ways to get to A state of some confusion:
- Go to Mrs. Plenty's Carnival, into the House of Mirrors, and then Gaze Into Dream's Mirror, which requires that you have at least one in Nightmares.
- Let your Nightmares quality increase to 8. You'll be taken there immediately.
A state of some confusion doesn't cost you any Echoes, but has a much worse action-efficiency compared to drinking laudanum. (Laudanum seems to do about 4 change points of Nightmares reduction, and actions in a state of some confusion are more like 1-2 change points of Nightmares reduction.) Not all actions there will decrease your Nightmares, but drinking laudanum will waste some of your time with curing your Wounds, so it's a wash; there's some good reasons to just let yourself go mad. Unfortunately, a few of the actions in confusion have a chance to abuse your four main qualities, and there are a few other small-ish drawbacks, so it's not all upside.
Option #2 if you have Memories of Light: we're all mad here, too.
If you have 10 Memories of Light, then you can spent two of them to go to the Mirror-Marches instead of A state of some confusion at the carnival. If you have at least one Memory of Light, then getting to 8 in Nightmares will take you here instead. The Mirror-Marches are much more generous than A state of some confusion; your main qualities won't be abused nearly as much, and actions that remove two or more points of Nightmares are much more common.
Option #3: Psychotherapy.
In your Lodgings, you'll get an option to Find a way to deal with your Nightmares if your Nightmares quality is 4 or higher. Spend a Sudden Insight (possibly gained via Invite a friend to join you in something terribly intellectual from your Lodgings), and you'll lose 5 change points of Nightmares. Your friend will gain one change point of Nightmares and also spend one action, so you should return the favor sooner or later.
Best Answer
In short: find a storylet that consumes your Fascinating quality. There should be something in Veilgarden involving the Struggling Artist, the Artist's Model, the Honey-sipping Heiress, or the Honey-sipping Jewel Thief that requires Fascinating; if you don't have enough Fascinating to play one of those storylets, build up your Fascinating further until you can.
In long: Fascinating is a "progress" quality, so the usual sequence is that you build it up to some level, then cash it in at a storylet that requires it. So you might build up your Fascinating up to 5, which will allow you to play a storylet that a) requires at least Fascinating 5, and b) whose success is based on how high your Fascinating is. If you like, you can spend extra actions increasing your Fascinating higher so that you have a better chance at success, because failure will usually decrease your Fascinating quality. (I don't recommend it, though; the extra actions you'd spend building up your Fascinating to increase the odds of success are better spent by simply taking the plunge, and spending a few actions to build up your Fascinating again if you fail.)
There is no way to simply dump your current Fascinating if you don't qualify for any Fascinating-related storylets. So if you're at some low level of Fascinating and can't cash it in right now, the only way to reduce your Fascinating is to build it up higher so you qualify for a storylet where you can cash it in.
If you've somehow managed to hit a sweet spot in your Persuasive quality where you can't build up your Fascinating, can't dump your Fascinating, and still want to get to Fascinating 0, there is an option: buy a Talkative Rattus Faber, from Nassos Zoologicals (in the Bazaar tab). That will give you -25 to all qualities while you have it equipped, so you can re-qualify for earlier storylets (and unequip it when you're done). When you're qualifying for storylets, you always use your current quality level, including the effects of equipment and pets.
Of random interest: You will eventually raise your Persuasive high enough that you no longer qualify for the Struggling Artist and Artist's Model stories. There are other stories that involve Fascinating: affairs at the Empress' Court, investigating a Tattooed Courier, and persuading clothes to cooperate on Polythreme. Did I mention that Polythreme is a bit weird?