If someone
walks a fine line between two activities or situations, or
treads a fine line between them, what they are doing is acceptable, but they are very close to the point at which it would become unacceptable.
At present we are walking a very fine line between getting away with it and having a very serious problem. The American will tread a fine line between freshness and a shortage of match fitness. Note: You can also say that you
walk or
tread a thin line between two things or that you
walk or
tread a narrow line between them.
He must tread a narrow line between investigation of his party's mistakes and charges of disloyalty. Compare with
a fine line between something.