In his essay “Politics and the English Language,” George Orwell famously mocked the use of not un- in English. His extreme example is, “A not unblack dog was chasing a not unsmall rabbit across a not ungreen field.” While this sentence is ridiculous, it’s also a straw man. Orwell and other English usage authorities are correct to disparage the use of not un- constructions in general, but there are exceptions, and not un- can be useful.
Examples
For example, some not un- constructions are useful for damning something with faint praise:
Effort’s gentleness and modesty are not unappealing, but these qualities simultaneously provide the picture with an underwhelming impact … [Variety]
The refried beans, while not unpleasant, were unlike any I’ve ever had … [Albany Times-Union]
And sometimes not un- constructions describe a middle ground for which neither the positive nor the negative term would be accurate—for example:
London’s buses are not unsuccessful, but they are now somehow deeply unlikeable. [London Evening Standard]
At 80 minutes, the set seemed short but not unsatisfying. [Minneapolis Star Tribune]
Its odor, musty but not unpleasant, is unlike anything else in the city … [New York Times]
But admittedly, we can find many examples of unjustifiable not un- constructions. These writers could drop the not un-‘s and use the positive words:
That’s not something you expect to get in what is essentially a kid’s film, but it’s not uninteresting and not unwelcome. [Chron]
This hot, early summer has brought us one not-unwelcome byproduct—an early crop of local tomatoes. [Atlanta Journal-Constitution]
The 19-year-old graduated with a not unimpressive 3.497 GPA … [E! Online]
In each of these cases, not un- hedges what the writer really means to say. Sometimes there is good reason to distance oneself from a sentiment (for example, when you’re trying not to overpraise a bad movie), but there is also something to be said for owning your assertions, and directness is usually better than indirectness.

