To further qualify my question: It is common parlance to say that the US (&UK) ousted Iranian Prime Minister Mossadeq in 1953. That they tried is undeniable. However, what is also undeniable is that the plan did not succeed at first. The coup leaders were arrested and the shah fled to Rome. Only days later, after massive protests, was Mossadeq ousted.

I have read different accounts of this event. Some (like Barr's "Lords of the Desert") highlight the CIA's role in bribing mobsters and religious leaders to organize anti-Mossadeq protests. Others (like Axworthy's "Revolutionary Iran") seem to think Western commentators overemphasize the CIA's role in what was really a domestic protest, led by bazaaris and the clergy, against the growing influence of the leftist Tudeh party.

What is the overall historians' consensus? How important was the US' role in orchestrating a coup in Iran?

Correction: I said Mossadeq was ousted "later in the year" when he was actually ousted four days after the first coup attempt.