Richard Cordray’s resignation as director of the Consumer Financial Protection Bureau provides a great opportunity for President Trump to appoint a new director who can undo an unfortunate legacy of bureaucratic overreach and political bias. More important going forward is what we have learned from our experience with the CFPB to prevent future similar missteps.

The first lesson is that Congress should never again create an “independent” agency with a sole director, particularly one not subject to the congressional appropriations...