  We examine k-essence models in which the Lagrangian p is a function only of
the derivatives of a scalar field phi and does not depend explicity on phi. The
evolution of phi for an arbitrary functional form for p can be given in terms
of an exact analytic solution. For quite general conditions on the functional
form of p, such models can evolve to a state characterized by a density scaling
with the scale factor as rho = rho_0 + rho_1(a/a_0)^{-3}, but with a sound
speed c_s^2 << 1 at all times. Such models can serve as a unified model for
dark matter and dark energy, while avoiding the problems of the generalized
Chaplygin gas models, which are due to a non-negligible sound speed in these
models. A dark energy component with c_s << 1 serves to suppress cosmic
microwave background fluctuations on large angular scales.
