The paper is concerned with the class of iterative methods
\[ x^{\delta}_{n+1}=x_n^{\delta}-g_{\alpha_n}(F^{\prime}(x_n^{\delta})^* F^{\prime}(x_n^{\delta}))F^{\prime}(x_n^{\delta})^*(F(x_n^{\delta})-y^{\delta}) \]
for solving nonlinear ill-posed problems \(F(x)=y\), \(\| y^{\delta}-y \| \leq \delta\), where \(F:X \to Y\) is a Fréchet differentiable operator between two Hilbert spaces. The iteration is terminated by the discrepancy principle
\[ \| F(x_{n_{\delta}}^{\delta})-y^{\delta}\| \leq \tau \delta< \| F(x_{n}^{\delta})-y^{\delta}\|, \quad 0 \leq n <n_{\delta},\;\tau>1. \]
Under certain conditions on \(\{ \alpha_n \}\) and the structural condition
\[ F^{\prime}(x)=R(x,{\overline x}) F^{\prime}({\overline x}),\quad\| I-R(x,{\overline x})\| \leq K_0 \| x-{\overline x}\| \]
on the operator \(F\), for a class of filter functions \(g_{\alpha_n}\) the convergence of \(x^{\delta}_{n_{\delta}}\) as \(\delta \to 0\) to the true solution is established. Under Hölder type source conditions, the order optimal rate of convergence estimates are derived.