We present an analytic expression of the harmonic bunching produced by the dispersive section of a free-electron laser (FEL) optical klystron operating in the high-gain exponential regime. This model allows the evaluation of the operating constraints and limits, the possible optimizations and advantages of such a device with respect to the conventional FEL configuration, i.e., shortening of the overall length and reduction of the induced energy spread, provided that the initial energy spread is smaller than the one required for the normal high-gain FEL operator. The analytical expressions derived here are confirmed by the numerical solution of the full nonlinear set of equations for the FEL.