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Analytical expressions for the plasmon resonance frequencies of prolate and oblate spheroids and their dependence on ellipticity are derived, and approximate bounds on these frequencies established. These formulas may be useful in tuning the plasmon resonance within certain limits. With increasing aspect ratio, the prolate spheroid resonance is red shifted relative to a sphere with no lower limit under the assumptions of a Drude dispersion model. On the other hand, the oblate resonances are blue shifted as the spheroid becomes increasingly flat, but up to a limit.