We present two model systems that are suitable for the study of bias in free-energy perturbation (FEP) calculations which are performed in molecular simulations. The models exhibit the asymmetry that is sometimes seen in these calculations, in which the magnitude of the bias is greater when the calculation is performed in one direction ( A-->B , sampling system A and perturbing into system B ) versus the other (B-->A) . Both models are formulated as a system of N independent particles, each sampling a space in the presence of a one-body field that is different for the A and B systems. In one model the field is a harmonic potential. The other model is discrete, such that each particle can be at one of two points (or states) of different energy. The neglected-tail bias model is applied to each system to estimate the average bias as a function of the amount of FEP sampling, and numerical calculations are performed to show that the bias model is effective. We show that the bias is significantly smaller when sampling is performed on the system having a broader work distribution (we designate this direction "insertion") compared to the bias for FEP calculations that sample the system with a narrower distribution ("deletion").