Three levels iterative technique for second kind Fredholm integral equations G.M.Attia, E.M.Ibrahim, Fathi M.H.Youssef, R.A. Abd El-Monem Abstract In this paper a new technique is proposed to modify the iterative methods of Atkinson-Brakhage. The proposed technique reduces the number of operations in each iteration more than those of Atkinson iterative method - 2, by using three levels of quadrature rules. This modification reduces the required time of computation to achieve the desired accuracy. It is known that Atkinson iterative method - 1 is superior in accuracy when $\lambda$ tends to zero or eigenvalue and iterative method - 2 is superior for $\lambda$ away from zero. The proposed technique moves between the two methods, therefore it is superior in accuracy for all values of $\lambda$ even when it is close to or away from zero.