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Exponential propagation iterative methods of Runge-Kutta type (EPIRK) provide a flexible framework to derive efficient

exponential integrators for different types of ODE systems. Here we develop new classes of EPIRK methods depending on

the properties of the equations to be solved. We derive the order conditions for the new classes of integrators and present new approaches to solving the order conditions where we optimize coefficients to construct more efficient schemes. Performance comparisons are conducted on a set of test problems to demonstrate the computational advantages of the new schemes themselves and the overall improvement in computational cost due to the recent additions to the EPIRK family.