Much of our understanding of ocean frontal dynamics follows from an approximation of the ocean fronts as straight. Baroclinic instability has traditionally been examined using a model of a front in approximate geostrophic and hydrostatic balance–i.e., a straight front in thermal wind balance. However, meandering fronts and mesoscale eddies dominate the global ocean, hence it is critical that we understand the effect of curvature. We study the effect of small curvature on baroclinic instability models of Eady and Charney and find that the effect of curvature principally arises through the modification of the potential vorticity (PV) gradient. Consequently, although curvature enters the Eady model via the introduction of Green modes, it does not actually modify the most unstable mode. In Charney’s model, however, the curvature of the flow introduces a depth scale that governs the vertical extent of the unstable modes and whose importance often presides over the planetary beta. We also find that the introduction of curvature in Charney’s model increases the horizontal wavenumber of the most unstable mode.