Coordinating conjunction immediately followed by parenthetical — Is a comma needed or not?

I don't have a membership to the CMS, so I can't speak to their take on it. But I would say that the meaning, or at least the tone that you're trying to communicate it subtly different between the two phrases. In your punctuation, the speaker is expressing doubt that "we are prepared to act promptly", and perhaps expressing the subjunctive as a bit of an aside.

And if the actual meaning is different, then rules of usage be damned. I personally would punctuate it thusly:

The situation is perilous; but - if we are prepared to act promptly - there is still one chance of escape.

No commas at all.

"Well, Stunk's Rules of Usage says that you're wrong. No comma."

"no comma is needed" does not mean "it is wrong to use a comma."

I was once an editor of a law review journal. I did not find Strunk helpful as to this issue. Generally, I would insert a comma after the conjunction but, for the sake of clarity, I would not place a comma before the conjunction. My wife, an English major and also a lawyer, however, disagrees with me. Of all of the grammar issues we have ever discussed, this is the only issue upon which we disagree.

Well my wife just showed me the new Chicago Manuel of Style. According to provisions 6.28 and 6.32, I lose the argument. As always, she wins. Do not insert a comma after a conjunction, but according to the Chicago Manuel of Style, you should insert a comma before the conjunction.

------ Strunk and White - rule 4

In their rule 4, Strunk and White (and I believe the OP's question too) refer to complex compound structures only, and only those that follow pattern such as this:

[independent clause 1] , [conjunction] (,) [dependent clause to independent clause 2 - introductory clause] , [independent clause 2] .

As do many other authoritative source, Strunk and White state that the second comma (the one in parentheses) should not be used. And for a good reason, too.

Not every pair of commas indicates that the element they surround is non-essential to the sentence or parenthetic. The first comma in the example above separates two independent clauses, and the second one indicates the boundary of a dependent clause that precedes its main (independent) clause. The rule that governs these commas is rule 4: "Place a comma before and or but introducing an independent clause" (the first comma in the example). The commas Strunk and White discuss in this rule are not parenthetic commas (and there are very few dependent clauses that are parenthetic, anyway). However, this advice is valid, widely followed, and is equally correct for parenthetic elements too (as I'll explain below). It is very rare indeed that you'd have a comma immediately following a coordinating conjunction such as and or but.

This rule is for complex compound sentences such as outlined above, where two independent clauses are joined by a coordinating conjunctions "and" or "but" (and a few other conjunctions that are outlined later on in the rule) and where the conjunction is followed by a dependent clause, or an introductory phrase requiring to be set off by a comma, which precedes the second independent clause.

Unlike some answers here suggest, adverbs are a different case altogether.

------ Strunk and White - rule 3

This rule refers to any parenthetic expressions that need to be set off by commas, when a conjunction precedes the parenthetic expression. (Not every parenthetic expression needs to be set off by commas or set off all.) The rule applies to constructions such as but not limited to:

[Subject] [predicate 1] , [coordinating conjunction] (comma here would not be grammatically correct) [parenthetic expression] , [predicate 2] .

E.g.:

She said her farewells, and despite the earlier disagreement, gave me a hug. (Matches the pattern Strunk and White use as an example.) or He would stay for the main course, and if it would please his mother, dessert. (The pattern here is different, but the same rule still applies.)

If it were not for the parenthetic expressions, the commas before the conjunction in the examples above would constitute a grammatical blunder (except when required for clarity, which in those examples they are not) because in the first sentence it'd split a compound predicate, and in the second, compound object. And yet according to the rule, when an expression is parenthetic, making it look like one (with commas on each end) should be so low on the priority list that even the compound predicate and compound object can be made to adjust split, just as long as we avoid a comma after the conjunction - avoiding a comma after the conjunction is THAT important.

So, even when the expression is parenthetic (i.e. not essential to the meaning of the sentence), if the commas are necessary to set it off, the commas don't actually need to look parenthetic - the conjunction is also enclosed within the commas: the commas are for clarity and not to tell the reader to skip what's between them if the reader feels so inclined. No-one who reads anything such as examples above pauses to think: "Hang on! Surely if I remove what's between the commas the sentence won't make sense!" When I read such sentences, the first of the commas goes unnoticed altogether, and the second one is where a natural pause would be, and if it aids clarity, the second comma is very helpful.

A writer may suggest that not every expression following a conjunction is parenthetic (or non-essential), and some could be essential to the meaning of the sentence. When you need to set off an essential expression with a pair of commas, I would argue that the same rule still applies. If we're not concerned with making parenthetic expressions look as such, why would we do that to non-parenthetic ones?

E.g.:

1. He always brought me dinner (,) and on Sundays (,) stayed to cook it himself.
2. He worked every day (,) and if necessary (,) stayed the night too.
3. The children played noisily (,) and when asked to stop (,) didn't pay any attention to any such requests.
4. He always moved around the office at a leisurely pace, and only when his phone sounded that special ringtone, ran towards his desk.

The "on Sundays," "if necessary," and "when asked to stop" phrases are all essential to the meaning of the sentences 1-3, as is the clause "when his phone sounded that special ringtone" to sentence 4. Not all introductory elements need to be set of by commas, and I don't see any clarity problems problem with examples 1-3 not using any commas at all (though there may be reasons other than clarity to add them), but the example 4 definitely needs something that would help the reader.

If a non-parenthetic introductory element that needs to be set off by commas follows a conjunction, it's logical to assume that the same rule applies because, if we're not concerned about making a parenthetic expression look like one, then making a non-parenthetic expression look like a parenthetic element is just illogical, if not downright bonkers. But do we need the first comma, before the conjunction or do we only need the second comma? Yes, we need both: try the sentences with the second comma only, and you'll quickly see why you need the first one too.

How will the reader tell the difference better what's essential and what's not in the sentence? I think the reader is smarter than we may assume, and I don't think we need to worry about him misunderstanding the meaning. If there's a risk of misunderstanding, I think the problem is with the composition or the sentence structure.

------ Comma After Conjunction which Begins a Sentence and is Followed by an Introductory Expression

This is a very sparsely covered subject. Most sources will state that only in very rare cases a comma after conjunction and before the introductory expression is needed, but where exactly - no-one seems to be sure.

Everywhere says that such a comma is only justifiable in very rare cases. In my writing, I very rarely feel that a comma is necessary after a sentence-beginning conjunction and before the introductory expression that follows it. Most of the time, I don't see that such a comma adds anything to the clarity or alters the meaning of the sentence at all. I searched and searched for guidance on this, and this is the only source that I could find that makes any sense: "Include commas after coordinating conjunctions that start sentences only when a nonessential phrase or a parenthetical follows the conjunction." (Introduce Me with a Comma by Beth Hill, August 2015) I can see why the two examples provided by the blog author call for such a comma.

"Or, she wanted to know, had I left my husband?

"Yet, and this is crucial, I’d forgotten to pack my pistol."

The author says it's "a nonessential phrase or a parenthetical", but there's also clarity: remove the first comma, and the reader may need to go over the sentence more than once to understand what you're trying to say.

At the moment, unless clarity is at stake I choose to never put a comma after a sentence-starting conjunction followed by an introductory or a parenthetical expression. In my reading of novels by authors whom I love and trust, I have not seen such commas at all. (But I will continue looking.)

------ The Impression I Get

From what I see in editors' blogs and style guides, the general consensus seems to be that a comma after a conjunction makes for inelegant writing and is spurious. Some say that such commas were acceptable before but are now viewed as pedantic. I read somewhere that, although such practice was religiously adhered to many years ago and by many classical writers too, in current climate of trend toward minimal punctuation it makes for a clumsy-looking sentences, mashed your reader stumble over too many commas that don't add anything, and makes the writer look ignorant. And I agree. And just go over Lynne Truss's "Eats Shoots and Leaves" or Caroline Taggard's "My Grammar and I (Or Should That Be 'Me'?)" or Steven King's "On Writing" - anybody who's anybody in writing echoes or quotes Strunk and White. And I don't think that any of us here are in a position where to dispute Strunk and White, CMS, Fowler etc.

This is to address the parenthetic argument and to show that not all dependent clauses starting with subordinating conjunction are parenthetic. My previous answer explains why whether it's parenthetic or not has nothing to do with the punctuation question such as the OP's.

Let's reverse the order by putting the dependent clause after the main add it's commonplace to do. The punctuation guidelines for dependent clause following its main clause is no comma before the subordinating conjunction - unless the dependent clause is parenthetical, which it rarely is.

CONSIDER THE EXAMPLES

A. Non-parenthetic (The if-clause cannot be removed without altering the meaning of the sentence. It provides essential information.) The event can go ahead if the rainclouds keep away.

vs.

B. Parenthetic (The if-clause can be removed, placed in parentheses, or set of with dashes -depending on author's intent - because it provides additional information.) The event can go ahead on a dry day, if the rainclouds keep away.

And so on:

A. Leanne treated him as a criminal deserved to be treated. vs. B. Leanne treated him with a shadow of contempt, as a criminal deserved to be treated.

A. He divorced before he went to jail. vs. B. He divorced in 1996, before he went to jail.

A. She said she would take on the project if she was given enough time. vs. B. She said she would take on the project with a reasonable deadline, if she was given enough time.

Parenthetic clauses starting with subordinating conjunctions (B) are always separated by a comma from their main clause, despite the general sweeping guidelines of not putting a comma before a subordinating conjunction which follows a main clause. (Try removing commas from Bs, and the meaning changes or becomes confusing.) Also, as Bs are parentheticals that clarify or add to what immediately precedes them, you cannot move them out to the front of the sentence without rendering the sentence ridiculous. (I am not even sure if you could call these Bs dependent clauses.) But if something can be moved to the front, it does not mean it's non-parenthetic, and some sentences don't suffer when a parenthetic clause starting with a subordinating conjunction is moved to the beginning. (Try doing it with these: "He finally went to jail, after 10 years on the run" or "He would drag himself home at dawn, if he could still walk by that time." Parenthetical? Yes. Can be moved to the front of the sentence? Yes.) The parenthetical can be moved to the front without much affecting the meaning. But all the B examples above contain dependent elements that are parenthetic: they are all extra information, clarification, or afterthought. All of the As give information you cannot derive anywhere else in the sentence or that which is essential to the nature of the notion being expressed. That's the difference.

The OP's example (which is from Strunk and White) indicates that the one chance of success exists only if prompt action is considered. And really this one can be either. Sometime it's difficult to decide whether an expression is parenthetic or essential, and when punctuating such cases, an author would go with what his intended meaning is and punctuate appropriately - putting a comma before the subordinating conjunction that follows the main clause, as in Bs above.

In most of the As, though, the dependent non-parenthetic clauses can be moved to the front of the sentence, and such a transposition would let the sentence retain the meaning while giving a different tone to what is being said. However, transposition does not make any of these dependent clauses parenthetic, but merely introductory: without them the sentences do not at all say the same thing, and most of the examples provided don't even make sense.

So a clause starting with a subordinating conjunction, transposed to the beginning of the sentence can be parenthetic / non-essential (or defining in case of relative conjunctions) or essential (or non-defining in case of relative conjunctions). But if we go back to the OP's question, the of-clause being parenthetic or essential such as so:

He was convicted, and before he went to jail, he divorced. (Could be argued essential or non essential depending on context which is missing.) She maintained that she rejected the task because of its unreasonable deadline, but if she was given enough time, she said she would take on the project. (Essential.) The fair will be outdoors, and if the rainclouds keep away, it will go ahead. (Essential.)

But the parenthetical argument doesn't change anything for the point at hand (punctuating a coordinating conjunction preceeding such a clause), because that first comma still goes BEFORE the coordinating conjunction and never after it, unless clarity is at stake - then both commas are included in complex compound sentences where two independent clauses are joined by a coordinating conjunction. But the same is true whether the comma before the joining coordinating conjunction would be grammatical (compound sentence where the conjunction separates two independent clauses) or not (two-part compound predicate or compound object or two-item list) without the introductory clause. But of course, the OP's question seemed to refer to cases as the first one:

[main clause 1] , [coordinating conjunction] ( comma or no comma?) [subordinating conjunction] [dependent or parenthetical poor introductory element for m. clause 2] , [main clause 2]

And I pointed out that some examples didn't match the pattern because, of course, a question of putting a comma before a coordinating conjunction preceding an introductory clause, parenthetic or not, usually arises only where complex or complex compound sentence is discussed. There is a trend of moving the first comma to after the coordinating conjunction on grounds of parenthesis, so here I point out that parenthesis had nothing to do with it, and whether parenthesis or not, the rule is the same: no comma after And or But.

(Please forgive any typos or autocorrect errors. This is put together on a tablet.)