In many situations, it has been observed that significant convergence improvements can be achieved in preconditioned Krylov subspace methods by enriching them with some spectral information. On the other hand, effective preconditioning strategies are often designed where the preconditioner varies from one step to the next so that a flexible Krylov solver is required. In this paper, we present a new numerical technique for nonsymmetric problems that combines these two features. We illustrate the numerical behavior of the new solver both on a set of small academic test examples as well as on large industrial simulation arising in wave propagation simulations.