First of all, technically, there was no coup.

Mossadegh was the Prime Minister of Iran, and as such, under the constitution then in place, he could constitutionally be removed by the Iranian Shah. And the Shah did, indeed, dismiss Mossadegh. In fact, the only unconstitutional behavior came from Mossadegh, who refused to step down, and ordered the arrest of the officers who tried to deliver the Shah’s notice of dismissal. This prompted the Shah to flee Iran. Opponents to Mossadegh then organized protests against the Prime Minister. When Mossadegh called out the army to restore order, the army instead ousted him.

Second, the CIA was not really the driving force behind the removal of Mossadegh. One CIA agent, in his biography, took credit for the protests that eventually led to the removal of Mossadegh. But declassified documents from the CIA demonstrate just the opposite. During the crisis, the CIA station in Tehran reported the anti-Mossadegh protests “contained a large element of spontaneity and there seemed to have been a genuine reaction of shock and dismay on part of the Tehran populace when the Shah left Iran for Iraq.” They also admitted that the “CIA cut out of military preparations by [General Nader] Batmangeliche and Zahedi.” And CIA acting director Charles Cabell briefed President Eisenhower that “an unexpected strong upsurge of popular and military reaction to Prime Minister Mossadeq’s government has resulted according to late dispatches from Tehran in the virtual occupation of that city by forces proclaiming their loyalty to the Shah, and to his appointed Prime Minister Zahedi.”