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Large-scale tropical phenomena such as the Madden-Julian Oscillation (MJO) and El Nino-Southern Oscillation (ENSO) are often studied using the longwave approximation to equatorial β-plane theory. This approximation involves the neglect of the (∂v/∂t) term in the meridional momentum equation. The approximation does not distort Kelvin waves, completely filters inertia-gravity waves, is reasonably accurate for long Rossby waves, but greatly distorts short Rossby waves. Here we present an improvement of the longwave model, based on an approximation of the (∂v/∂t) term rather than its complete neglect. The new model is similar to the longwave model in the sense that it does not distort Kelvin waves and completely filters inertia-gravity waves. However, it differs from the longwave model in the sense that it accurately describes Rossby waves of all wavelengths, thus making it a useful tool for the study of a wider range of tropical phenomena than just the MJO and ENSO. Although most of the mathematical analysis performed here is in the context of equatorial β-plane theory, we briefly discuss how the ideas can be generalized to spherical geometry.