  We explore various pitfalls and challenges in determining the
equation-of-state (w) of dark energy component that dominates the universe and
causes the current accelerated expansion. We demonstrated in an earlier paper
the existence of a degeneracy that makes it impossible to resolve well the
value of w or its time-derivative with supernovae data. Here we consider
standard practices, such as assuming priors that w is constant or greater than
-1, and show that they also can lead to gross errors in estimating the true
equation-of-state. We further consider combining measurements of the cosmic
microwave background anisotropy and the Alcock-Paczynski test with supernovae
data and find that the improvement in resolving the time-derivative of w is
marginal, although the combination can constrain its present value perhaps to
20 percent uncertainty.
