We present interplanetary network localization, spectral, and time history information for four short-duration, hard spectrum gamma-ray bursts, GRB000607, 001025B, 001204, and 010119. All of these events were followed up with sensitive radio and optical observations (the first and only such bursts to be followed up in the radio to date), but no detections were made, demonstrating that the short bursts do not have anomalously intense afterglows. We discuss the upper limits, and show that the lack of observable counterparts is consistent both with the hypothesis that the afterglow behavior of the short bursts is like that of the long duration bursts, many of which similarly have no detectable afterglows, as well as with the hypothesis that the short bursts have no detectable afterglows at all. Small number statistics do not allow a clear choice between these alternatives, but given the present detection rates of various missions, we show that progress can be expected in the near future.
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