Opposite of "loosely-based"

We often see a screenplay noted to be “loosely based” on a novel or true story. This usually means significant portions of the story, or major plot turns, have been rewritten. Sometimes even major characters are dropped or added.

What is the opposite of that phrase, something that mostly has fidelity to the original but may differ is some relatively minor points?

To be used in a context where we want to provide disclosure about imperfect fidelity, but we do not want to draw too much attention or be overly dramatic about the differences.

I thought of “closely based”, but that does not sound right.

"Faithfully" comes to mind. As in "faithfully adheres to the events of the original text," etc.

Simply say that a screenplay was adapted from a book:

adapt, tr.v: to change a book or play so that it can be made into a movie, TV program, etc. [MacMillan]

This encompasses any minor changes necessary to accommodate the different ways that books and movies tell stories.