Stiff Convergent Problems are the ones that have some modes that converge very slowly when solved using iterative techniques. Mode pushing (MP), superimposed on these techniques, is a method of accelerating convergence of only these modes. This paper discusses the theory of the MP method and a practical algorithm which estimates the stiff convergent eigenfunctions and uses them to accelerate the convergence of the iterative process. The estimation process can also be extended to the case of two or more stiff modes. It is seen that the complexity of the estimation process increases with number of modes to be estimated.