Geant4 Application for Emission Tomography (GATE) is a widely used, well-validated and very versatile application for Monte Carlo simulations in emission tomography. However, its computational performance is poor, especially for voxelized phantoms, partly due to the use of a very general particle tracking algorithm. In this work, two methods are proposed to reduce the time spent on particle tracking in the phantom: a newly introduced 'regular navigation algorithm' of Geant4 and fictitious interaction tracking (also known as Woodcock tracking) for photons. The speed-up introduced by the two methods was investigated by simulating a PET acquisition with the Allegro/GEMINI GXL PET/CT scanner. The simulation was based on a clinical head-and-neck [(18)F]FDG PET/CT scan. The total time spent for the simulation (including initialization, particle tracking and signal processing) was obtained for seven settings corresponding to different tracking options. All seven methods led to very close results with regard to the total number of detected coincidences (less than 0.5% differences), and trues, scatter and random fractions. Acceleration factors of approximately 2.7 (14 x 14 x 9 voxels) to 27.6 (378 x 378 x 243 voxels) were obtained in comparison with the fastest available tracking available in GATE 3.1.2.