Phrase "to no avail" and commas

The phrase "to no avail" describes something that is futile or ineffective.

His efforts to stop the thief were to no avail.

Commonly, the phrase is separated from the independent clause of the sentence by a comma. Is this a violation, seeing as the phrase is not independent per se?

She tried to brush the tangles out of her hair, but to no avail.

She tried to brush the tangles out of her hair but to no avail.

Even when writing, I myself would not worry about throwing in the comma as I have never met any reader who finds something to pick at in a sentence like the one above. In a slightly more formal context, would the phrase be connected with or without a comma?

Solution 1:

Two British dictionaries define the word, with example sentences, as follows:

avail
noun (usually in phrase of/to no avail)
Use or benefit:
he begged her to reconsider, but to no avail
My protestations about the lack of evidence of benefit in such procedures were to no avail.
She was doing a sterling job of trying to wake him up but to no avail.
After a few frantic phone calls to no avail, the decision to ad-lib was made.
[Note: The corresponding American English entry in this dictionary did not include this usage.]

avail
noun [uncountable]
use, purpose, advantage, or profit:
We tried to persuade her not to resign, but to no avail (= did not succeed).
My attempts to improve the situation were of little/no avail.
[Note: The corresponding American English entry in this dictionary did not include the word 'avail' at all.]

You will see that, of the three example sentences terminating in "but to no avail", two precede it with a comma, and one doesn't. Personally, I would normally include a comma in that position, because, when speaking the sentence, I would normally pause slightly at that point. As John Lawler says in his comment, if you want the reader to 'hear' the pause, then include a comma.