We have explored high power microwave ((lambda) equals 1.5 mm) pulse amplification along a tapered undulator FEL using the 1D Compton FEL equations with slippage. For an appropriate taper, sideband instabilities are suppressed and a short (approximately 50 psec) Gaussian pulse will propagate in a nearly self-similar way as it grows in power, slipping through a much longer electron pulse (beam energy, 750kV; current, 100A; radius equals 2 mm; length equals 200 radiation periods). This is in contrast to the example of pulse propagation in a constant parameter undulator, where the Gaussian pulse breaks up into irregularities identified with sidebanding. Variation of initial pulse width shows convergence to a 50 psec wide output pulse. Because of the slippage of the radiation pulse through the electron pulse, the peak microwave pulse intensity, approximately 3GW/cm2, is about three times the kinetic energy density of the electron beam.