  We study decoherence in a qubit with the distance between the two levels
affected by random flips of bistable fluctuators. For the case of a single
fluctuator we evaluate explicitly an exact expression for the phase-memory
decay in the echo experiment with a resonant ac excitation. The echo signal as
a function of time shows a sequence of plateaus. The position and the height of
the plateaus can be used to extract the fluctuator switching rate \gamma and
its coupling strength v. At small times the logarithm of the echo signal is
proportional to t^3. The plateaus disappear when the decoherence is induced by
many fluctuators. In this case the echo signal depends on the distribution of
the fluctuators parameters. According to our analysis, the results
significantly deviate from those obtained in the Gaussian model as soon as v
greater than \gamma.
