To determine appropriate influenza pandemic containment and mitigation measures, health authorities need to know the approximate case fatality ratio (CFR) for this new infection. We present four different methods for very provisionally estimating the plausible range of the CFR for symptomatic infection by this pandemic strain in developed countries. All of the methods produce substantially lower values (range 0.06% to 0.0004%) than a previously published estimate for Mexico (0.4%). As these results have many limitations, improved surveillance and serological surveys are needed in both developed and developing countries to produce more accurate estimates.