In previous years, the council established funding thresholds so that no institution suffered cash reductions of more than a certain amount - 4.5 per cent in cash terms last year.
This year, help has been phased in, using a sliding scale subject to a Pounds 20,000 threshold.
It means that institutions which would otherwise receive more than 10 per cent below last year's allocation will in fact have their funding reduced by no more than 1 per cent.
By the same token, institutions which would have received an 8 per cent funding increase will only receive 7 per cent.
The council stresses that this is intended as a short-term measure, which will be phased out over at most three years.
Institutions which receive more than Pounds 500,000 or 4 per cent of their funding this way will have to agree with the council on how to manage future funding losses.