The phrase "a very specific circumstance" is correct and usable in written English.
You can use it when referring to a particular situation that is detailed or defined in a precise way.
Example: "In a very specific circumstance, the rules may be adjusted to accommodate unique needs."
Alternatives: "a particular situation" or "a distinct scenario".
As I mentioned in our initial impressions video, the Note's S Pen only seems worthwhile in a few very specific circumstances.
It's very difficult for me to say that the way I approach investments is particularly different than the way he does unless in a few very specific circumstances where we investigated companies manufacturing birth control pills or organic tampons, for instance.
For a limited time, under very specific circumstances.
The cougar cannot be legally killed without a permit in California except under very specific circumstances, such as when a cougar is in act of pursuing livestock or domestic animals, or is declared a threat to public safety.
It's also another way Waze is doing a sly, indirect end-around on Uber; the Google-owned company's Carpool is a ride-hailing competitor in certain, very specific circumstances, and Order Ahead could fit a similar niche in the realm of on-demand food, where UberEATS also operates.
A child of an American citizen mother born abroad is an America citizen, absent some very specific circumstances that even Trump isn't challenging.
Since your fainting occurs in very specific circumstances, a combination of these factors may work together to exacerbate your low blood pressure.
Personally, I am by expertise and experience a humanitarian specialist, so I'm always on the lookout for new ideas that can work in the very specific circumstances of a sudden crisis or in the complexity of a protracted, violent conflict.
This allows for controlled testing of an algorithm's robustness under very specific circumstances.
