In May 1977, Washington Senator Henry M. Jackson named Stennis as one of the senators who was part of a bipartisan attempt to develop, in reference to the SALTII treaty, "the kind of agreement that... will stabilize the situation in the world." By May 1979, the "New York Times" wrote that Stennis was one of the moderate senators who would swing the vote on the SALTII treaty and along with West Virginia Senator Robert Byrd was viewed as "possibly timing their decisions to influence other waverers". On June 19, Stennis, Robert Byrd, and Frank Church consented to the Senate Armed Services Committee holding separate hearings on SALTII on July 23, allowing the Senate Foreign Relations committee to have two weeks as the only committee reviewing the treaty.