The tug-of-war between Big Law firms and their most profitable corporate clients has shifted in favor of firms as they increasingly use advance conflict-of-interest waivers seeking to govern whether, and when, they can represent competing corporations at the same time, legal ethics experts say.

Courts increasingly are finding that firms devising advance waivers are taking care to be more specific so they can avoid being targeted by their own clients over conflicts—or at least can beat them in court when they get sued—experts also say.

Federal judges over the last 18 months have refused to disqualify leading law firms like …