Islam [Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992)] and Islam and co-workers [in Digest of Integrated Photonics Research (Optical Society of America, Washington, D.C., 1992)] have proposed adding a lumped gain to soliton dragging logic gates in order to relax the timing constraints. Three reduced models are used to study the dragging gate with discrete gain and are compared with complete simulations. The most accurate of these methods, the variational method with chirp, predicts the time shift of the control pulse with an accuracy within 12% at all initial separations of the control and signal pulses. This method also predicts an increase by a factor of 2 in the timing window, a result that is consistent with complete simulations and experiments.