WASHINGTON—A recent Justice Department crackdown on banks and other firms for foreign bribery, money laundering and manipulation of key interest and foreign exchange rates has prompted some changes but many companies still aren't doing enough to comply with U.S. law, said Mythili Raman, acting head of the Justice Department's criminal division.

Ms. Raman, who's overseen many of the department's cases, plans to announce Wednesday afternoon she'll leave the Justice Department next month after 18 years as a prosecutor. U.S. President...