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Branch-cut integrals are used to calculate the reflection of transient pulses from the surface of a cold, lossy, semi-infinite plasma. For the case considered in detail, small to moderate losses and an impulse-incident waveform with transverse magnetic polarization, the reflected waveform is oscillatory for small losses (collision rate much less than the plasma frequency) but decays monotonically for a collision rate of half the plasma frequency. The reversal of polarity of the initial half cycle of the reflected waveform observed as the incidence angle increases through 45° is interpreted as a Brewster-angle phenomenon.