Sometimes you just need a hyphen. You really do. Here’s proof:
He was a big-city worker, a cold-case officer with slicked-back hair.
is very different from
He was a big city worker, a cold case officer with slicked back hair.
In the first case we have an urbanite with a sleek coiffure who works on cold cases . In the second we have a large, chilly case officer with very tidy back hair who works for the city.
Are you convinced those hyphens are worth it?
Now, it isn’t necessary to hyphenate every compound adjective. When only one meaning is possible, those hyphens aren’t really necessary. This is the part where you use your discretion.
Sometimes you’ll see that a missing hyphen could radically change your message. Sometimes you’ll see that, although it won’t really change your message, those hyphens will prevent your reader from backtracking and rereading your sentence. Sometimes they won’t make any difference at all.
In my view, accuracy and ease of reading are both equally important. Of course I want the right message, but what good will it do if I chase off readers with hard-to-read prose? For that reason I tend to err on the side of caution in my use of hyphens.
When not to hyphenate:
When the adjective comes after the thing it describes: The hyphen is really only needed when the compound adjective comes before the thing it describes: while slicked back hair is confusing hair that’s slicked back isn’t.
When you have an adverb ending in -ly: Likewise, hyphens should be left out of any compounds formed with an adverb ending in -ly. There’s nothing confusing about an utterly baffling instruction manual (except the manual itself, of course!).