  We point out that quintessence with an exponential potential V_0 exp(- beta
phi / 3^{1/2} M_p) can account for the present observed acceleration of the
universe, without necessarily leading to eternal acceleration. This occurs for
2.4 < beta < 2.8. Thus a cosmological horizon, which is supposed to be
problematic within the context of string theory, can be avoided. We argue that
this class of models is not particularly fine-tuned. We further examine this
question in the context of a modified Friedmann equation, H^2 ~ rho + p, which
is suggested by higher dimensional self-tuning approaches to the cosmological
constant problem. It is shown that the self-tuning case can also be consistent
with observations, if 1.8 < beta < 2.4. Future observations of high-z
supernovae will be able to test whether beta lies in the desired range.
