Unlike Capt. Bonespurs, Mueller enlisted for Vietnam and was a highly decorated Marine.

After waiting a year so a knee injury could heal, Mueller was accepted for officer training in the United States Marine Corps in 1968, attending training at Parris Island, Officer Candidate School, Army Ranger School, and Army jump school. Of these, he said later that he considered Ranger School the most valuable because he felt “more than anything teaches you about how you react with no sleep and nothing to eat.”[27][28]

In the summer of 1968, he was sent to South Vietnam, where he served as a rifle platoon leader as a second lieutenant with Second Platoon, H Company, 2nd Battalion, 4th Marines, 3rd Marine Division.[10][29] On December 11, 1968, during an engagement in Operation Scotland II, he earned the Bronze Star with “V” device for combat valor for rescuing a wounded Marine under enemy fire during an ambush in which he saw half of his platoon become casualties.[30][31] In April 1969, he received an enemy gunshot wound in the thigh, recovered, and returned to lead his platoon until June 1969.[32] For his service in and during the Vietnam War, his military decorations and awards included additionally, the Purple Heart, two Navy and Marine Corps Commendation Medals with Combat “V”, Combat Action Ribbon, National Defense Service Medal, Vietnam Service Medal with four service stars, Republic of Vietnam Gallantry Cross, Republic of Vietnam Campaign Medal, and Parachutist Badge.

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Reflecting on his service in the Vietnam War, Mueller said, “I consider myself exceptionally lucky to have made it out of Vietnam. There were many—many—who did not. And perhaps because I did survive Vietnam, I have always felt compelled to contribute.”[35] In 2009, he told a writer that despite his other accomplishments, he was still “most proud the Marine Corps deemed me worthy of leading other Marines.”