  We place observational constraints on models with the late-time cosmic
acceleration based on a number of parametrizations allowing fast transitions
for the equation of state of dark energy. In addition to the model of Linder
and Huterer where the dark energy equation of state $w$ monotonically grows or
decreases in time, we propose two new parametrizations in which $w$ has an
extremum. We carry out the likelihood analysis with the three parametrizations
by using the observational data of supernovae type Ia, cosmic microwave
background, and baryon acoustic oscillations. Although the transient cosmic
acceleration models with fast transitions can give rise to the total chi square
smaller than that in the $\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model, these
models are not favored over $\Lambda$CDM when one uses the Akaike information
criterion which penalizes the extra degrees of freedom present in the
parametrizations.
