A very light scalar field can serve as a dynamical dark energy or quintessence. In the limiting case of a flat, non-zero scalar field potential, the influence on the cosmic expansion is indistinguishable from a cosmological constant. How close to this limiting case can we realistically expect to find scalar field dark energy? In this talk I will discuss some properties of scalar fields for which the cosmic equation-of-state (the ratio of the mean pressure to energy density) is in the neighborhood of -1, close to a cosmological constant.