We studied the effect of sampling density and randomness in Variable Density Poisson Disk (VDPD) undersampling patterns on Parallel Imaging Compressed Sensing (PICS) reconstruction errors. PICS reconstructions were performed on 3 datasets (knee, prostate, and brain) which were retrospectively undersampled with 110 VDPD undersampling patterns each. We found major differences in Normalized Root Mean Squared Errors when using different sampling densities, while the influence of randomness in patterns of the same sampling density was minor. Furthermore, the optimal sampling density varied per dataset. This shows that ad hoc choices of VDPD sampling density can result in significantly worse PICS reconstructions.