Well he also participated in the filibuster.
June 10, 1964
Civil Rights Filibuster Ended
At 9:51 on the morning of June 10, 1964, Senator Robert C. Byrd completed an address that he had begun 14 hours and 13 minutes earlier. The subject was the pending Civil Rights Act of 1964, a measure that occupied the Senate for 57 working days, including six Saturdays. A day earlier, Democratic Whip Hubert Humphrey, the bill's manager, concluded he had the 67 votes required at that time to end the debate.
And J.W. Fulbright, Bill Clinton's mentor.