PurposeAn iterative k‐space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields.Theory and MethodsThe spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k‐space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke‐based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments.ResultsThe method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate‐transformation and Jacobian‐based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity.ConclusionAn iterative method for designing k‐space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. Magn Reson Med 74:826–839, 2015. © 2014 Wiley Periodicals, Inc.