This is pretty minor, but my mind flagged it as I read, and I thought it might be an example of the reason it's good to keep sentences as simple as you can, to make that an actual part of revision.
Here's the sentence, from a NYT article on California's water problems (you Californians must feel like a plague of locusts is next)--
...(I)t was Mark Twain who was believed to have said, “Whiskey is for drinking; water is for fighting over” ....
What's wrong? Well, the awkwardness of that "who was believed" is a clue. It's actually introducing a new "character"-- the unidentified person or persons who believed Twain said that. Notice the passive construction-- well, how this forces a perfectly active subject/verb (Twain said) combo into passivity (Twain... was believed, and who believed is never stated, so passive), and then into some weird past perfect tense, and for what? To indicate that the reporter isn't sure Twain really said that? (I do understand-- I'm sure he never said a lot of the pithy quotes attributed to him.) But then also the past tense there -- was believed? So he's no longer believed?-- starts forcing questions on us (who believed that, do they still believe that), and why? Why construct a sentence that opens up so many irrelevant issues? If you want to use the quote, go ahead, but simplify the sentence so it says ONLY what you want it to say:
Twain said this maybe
Here's what he maybe said
What's the problem? Well, first, "it was Mark Twain" diminishes the sentence's true subject (Mark Twain, the one that did the action of saying) into a predicate nominative (what "it" was), thereby diminishing the importance of the most important word. There are reasons to use "it was" there-- for rhythm, for a longer sentence-- but the tradeoff is wordiness-- and an editor (obviously not the NYTimes editor:) will probably try to cut that and put Mark Twain in the pride of place-- the subject position.
Second, it's that darned relative clause:
... who was believed....
Relative clauses are adjectival usually, modifying a noun-- here Twain (they can be adverbial and modify a verb, but that's less common). Relative clauses start with a relative pronoun (usually who or which). Clauses of any kind take on more importance in the sentence just because they're clauses and have a subject and verb (Subject -- who, verb-- was believed). But that means that relative clauses (which are JUST modifiers, that is, not syntactically that important) often distract from the main clause of the sentence, especially when they break up the subject/verb sequence as here.
The first technique to trim and simplify a sentence is to decrease relative clauses to a modifying word or phrase. Doing that will put the emphasis back on the most important elements (subject and verb-- actor and action), and also get rid of that distracting and complicating clause in the middle of the sentence.
So how would I edit this? Well, the "who was believed" is really meant to say, "Twain is reputed to have said this." So go with an adverb that modifies the verb! After all, it's the verb (said) that you want to call into doubt, not Twain-- Twain did exist, so HE is not alleged. It's his saying this that is alleged. Also if I diminish this from a clause (which needs a verb and so tense) to an adverb, I just move around the issue of tense (is he still believed to have said that, or was it only in the past he was believed) by not presenting it as an issue in the "was".
Mark Twain supposedly (allegedly, reputedly) said, "===."
Or I might make the quote tag a dependent clause, and the quote the main clause, depending on whether I want the emphasis on Twain or the quote:
As Mark Twain allegedly said, “Whiskey is for drinking; water is for fighting over” ....
To simplify, determine what's important in the sentence, and make that or those the clauses, and avoid making the less important thoughts into clauses. Simple! :)