In July, both formally announced they would not seek reelection, although Bishop had said last cycle this term would be his last.
"It was a big one," said Bishop about his term limit factoring into his decision. "I would like to stay longer, but at the same time, six years is a good run."
With his characteristic wit, Bishop added: "We should leave before we are too tired to keep going."
Conaway likewise said term limits were a factor in his decision.
"In concept, it's good for the system. Bad for me personally, but good for the system," he said, adding: "In balance it's good for the system to allow younger folks to keep coming up. It keeps them in the fight longer."
In addition to Brady, there are two other Republican ranking members who will reach the term limit next year: Texas' Mac Thornberry on the Armed Services Committee, and Ohio's Steve Chabot on the Small Business Committee.
Chabot sought to vacate his role on Small Business this Congress to serve as the top Republican on the Judiciary Committee but he lost to Georgia Rep. Doug Collins.
Chabot may have another go at the Judiciary slot if Collins is appointed to the Georgia Senate seat Johnny Isakson is vacating at the end of the year.
Proponents say the negatives associated with limiting chairmen or ranking members to three terms are outweighed by the positives of keeping committees stacked with fresh faces and ideas and preventing a small group of members from consolidating power.
Former Rep. Howard "Buck" McKeon, R-Calif., announced in January 2014 he wouldn't run for reelection. At a news conference announcing his retirement, the then-Armed Services chairman said his term limit was the "biggest motivator" of his decision.