As one of three Republicans on the Senate Rules and Administration Committee, Cooper was involved with the investigation of Johnson aide Bobby Baker in 1964, which he decried as "a whitewash" after the committee blocked further investigation.
作为参议院规则和行政委员会的3名共和党议员之一，库珀于1964年同他人一起对约翰逊的助手鲍比·贝克（Bobby Baker）展开调查，但沃伦委员会之后就阻止了进一步调查，库珀对此谴责这是一种“撇清”行径。