The transport of small molecules across a phospholipid membrane is studied by molecular dynamics simulations. The effects of size, hydrophobicity, and asphericity of the penetrants on the permeation process are investigated. For this purpose, permeability coefficients of oxygen and ammonia are computed using an inhomogeneous solubility-diffusion model and compared to the previously computed results of the permeation of water. Furthermore, solubility and diffusion data are computed for a series of Lennard-Jones particles that differ in size and shape. The results are discussed within the framework of the four-region model and are especially related to the free volume characteristics of the membrane. It is concluded that the free energy of solvation mainly determines the shape of the permeation resistance profile. For hydrophobic particles the membrane interior will act as a trap instead of a barrier. Moderately hydrophilic and hydrophilic penetrants experience the largest resistance to permeation in the dense part of the lipid tail region. This region is therefore most important in discriminating between various penetrants.