We consider the adaptation of random early detection (RED) as a buffer management algorithm for TCP traffic in Internet gateways where different maximum transfer units (MTUs) are used. We studied the two RED variants described in [4] and point out a weakness in both. The first variant where the drop probability is independent from the packet size discriminates connections with smaller MTUs. The second variant results in a very high packet loss ratio (PLR), and as a consequence low goodput, for connections with higher MTUs. We show that fairness in terms of loss and goodput can be supplied through an appropriate setting of the RED algorithm.