Partial cross sections were measured for the ionization M+e~M"++(n+1)e for M=Kr and Xe (n = 1 -6) as a function of electron energy (0-470 eV). The experiment is based on a crossed-beam timeof-flight mass spectrometer employing pulsed electron and atomic beams, and pulsed ion extraction.Cross sections for Kr'+, Kr +, and Xe + have not been previously measured over this energy range. The cross sections reported for the remaining ions considerably narrow the uncertainty of previous measurements. The source of discrepancy among recent work appears to be due to improper account of detector-gain effects. The ionization onsets are fitted to threshold power-law expressions to derive ionization potentials.PACS number(s): 34.80.Dp, 35.10.Hn