An electrically driven shock wave is launched axially down a tube filled with Te = 1−2-eV plasma, carrying an axial current and associated azimuthal magnetic field (250 G). The number density is between 1016 and 1017 cm−3 and the shock Mach numbers range from 1.2 to 6.5. Flux compression of 10-25% at the front is observed, but this amount is very much smaller than ideal theory predicts and its duration is briefer. The flux increase is closely followed by diamagnetic discharge plasma producing an abrupt flux decrease. Mixing with this plasma and boundary-layer flow to the walls of the shock tube account for the small and brief field compression observed. Rough calculations support this picture and include an effective fraction q1 of the flow not undergoing compression. This q1 is found to be as high as 50%.