In a method for determining transmission coil-specific RF excitation pulses for component coils of a transmission coil array for accelerated, PPA-based volume-selective magnetic resonance excitation of a tissue region of a patient, and a magnetic resonance tomography apparatus operating according to the method, a first series of volume-selective RF excitation pulses along a first transmission trajectory in transmission κ-space is successively individually radiated by the component coils of the transmission coil array and the resulting magnetic resonance signals are received, and a second series of volume-selected RF excitation pulses along a further reduced transmission trajectory in transmission κ-space is simultaneously radiated by all component coils of the transmission coil array and the resulting magnetic resonance signals are received, and a complete transmission trajectory in transmission κ-space is then determined from which combination coefficients are calculated, and the coil specific RF excitation pulses are then calculated from the combination coefficients in order to produce a desired excitation profile.