His command comprised more than 34,000 USAF operational and support personnel stationed at eight major bases and more than 87 facilities principally located in Japan, South Korea, the Philippines and Hawaii.

When the U.S. Air Force Academy opened in 1955 in temporary facilities at Lowry AFB, Colorado, Braswell was assigned as commander of one of the original four cadet squadrons and served in that capacity for three years.

Braswell returned to the United States in August 1961 to attend the Air Command and Staff College at Maxwell AFB, Alabama.

Following his return from Southeast Asia in August 1968, Braswell became the director of operations for the 4th Tactical Fighter Wing at Seymour Johnson AFB in North Carolina.

Braswell was assigned to Supreme Headquarters Allied Powers Europe, Belgium, as assistant chief of staff for operations from September 1974 to June 1977.

In July 1977 he was promoted to lieutenant general and returned to the United States as Director for Plans and Policy (J-5), Organization of the Joint Chiefs of Staff in the Pentagon.

In this capacity he helped guide ground-breaking negotiations with major environmental groups to write and propose to Congress legislation establishing national mandatory efficiency standards for energy-consuming appliances.

Under his guidance ARI also coordinated extensive research by industry companies to develop and employ new refrigerants that would not damage the protective ozone layer in the upper atmosphere.