Cohorts of 3-6 patients receive escalating doses of interleukin-13 PE38QQR immunotoxin until the previously-defined HEC is reached or MTD is determined, whichever occurs first. If dose-escalation is stopped after HEC is reached, then three additional cohorts of patients receive escalating durations (5, 6, or 7 days) of post-resection infusion. If dose escalation is stopped after the MTD is determined, then the duration of post-resection infusion is not escalated.