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This paper reports on the relative vulnerabilities of bare- and insulated-line conductors to hits from discharge strokes coming from sources at voltages too high to prevent flashovers, like lightning. Protection against such strokes must be based on diversion strategies, where the conductor to be protected is made as unattractive as possible compared to alternative, usually grounded conductors nearby. As a first attempt to quantify this discharge-stroke susceptibility for some commonly used line conductors, we have performed measurements where high-voltage impulses, applied to a rod 1-2 m above a ground plane, launch streamer-leader sequences propagating downwards toward a wire or insulated cable or both, suspended horizontally 0.25-0.5 m above the ground plane. The ensuing spark will thus always have a dual choice, either between the wire/cable and ground, or between the wire and the cable. The percentage of spark hits to the wire/cable is counted and plotted as a function of the sideways displacement of the wire/cable from the rod axis, and is a measure of the "spark appeal" of the wire/cable. The measurements confirm that streamers emitted from an object are especially important for attracting sparks from negative sources. Our results indicate that three-phase overhead lines should be as thick and as closely spaced as possible to minimize lightning-stroke risks. The effect of line insulation is both to increase the effective thickness and to permit closer spacing between the phases.