In cosmological simulations, it is found that the degree of fragmentation of the Population III (Pop III) protostellar disk varies strongly from halo to halo. This is to be expected if turbulence within the cloud plays a role in determining when and where fragmentation actually occurs. It is also reasonable to expect that the amount of angular momentum present at small-scales will have a large impact on Population III protostellar disk formation and evolution. We conducted a numerical study with the Voronoi moving-mesh AREPO in which we examined how different levels of initial subsonic turbulence and rotation within the star-forming cloud affect the outcome of Pop III star formation in terms of the total number of objects formed, the overall mass spectrum and the individual accretion history. We used controlled initial conditions which examine the collapse of a gas cloud with pre-defined levels of turbulence or rotation within a small computational box. This allowed us to draw conclusions on the specific role, strength and importance of the particular physical parameters applied here. In this talk, I will present some of our results and discuss the relevance of our numerical approach in which we have performed several realizations per combination of initial conditions and have averaged over the realizations instead of just considering single, individual runs.