Cooper continued to be an independent voice in the Senate. During the Red Scare, he was critical of attempts to permit illegal wiretap evidence in federal courts and attempts to reduce the protections against self-incrimination granted by the Fifth Amendment. Nevertheless, he refused to strip Joseph McCarthy, the leading figure in the Red Scare, of his major Senate committee chairmanships, cautioning that "many of those who bitterly oppose Senator McCarthy call for the same tactics that they charge him with." He was the only Republican to oppose the Bricker Amendment, which would have limited the president's treaty-making power. He concluded that the issues addressed by the amendment were not sufficient to warrant a change to the Constitution. He also opposed the Submerged Lands Act and the Mexican Farm Labor bill, both of which were supported by the Eisenhower administration. He denounced Eisenhower's appointment of Albert M. Cole, an open opponent of public housing, as Federal Housing Administrator and opposed many of the agricultural reforms proposed by Eisenhower's Agriculture Secretary, Ezra Taft Benson. Again, his independence did little to diminish his stature in the party. In 1954, he was named to the Senate Republican Policy Committee.