William Strunk's Rules of Usage states:
If a dependent clause, or an introductory phrase requiring to be set off by a comma, precedes the second independent clause, no comma is needed after the conjunction.
Strunk's example illustrates the point:
The situation is perilous, but if we are prepared to act promptly, there is still one chance of escape.
However, I would be tempted to put a comma after the "but," like this:
The situation is perilous, but, if we are prepared to act promptly, there is still one chance of escape.
So, I know you're thinking, "Well, Strunk's Rules of Usage says that you're wrong. No comma."
But is Rules of Usage really the best source? I'd like to see this rule in a more contemporary and authoritative source, like the Chicago Manual of Style.
There are many instances — such as in The New York Times — where the comma is included before a parenthetical comment that comes after a coordinating conjunction.
Any authoritative source on the issue?