Three patients will be entered at each dose level. The dose of alemtuzumab will be escalated if these 3 patients complete the 4-week treatment and none experience a DLT by week 12 of therapy. If 1 of 3 patients treated at a given dose level experiences a DLT, then 3 more patients are treated at that dose level. If the incidence of DLT among those 6 patients is 1 in 6, then dose escalation to the next highest dose level occurs. If 2 or more of the 6 patients treated at a dose level experience DLT, then the MTD is considered to have been exceeded. At that point, unless 6 patients were treated at the previous dose level, 3 further patients will be treated at that level, and the same principles for determination of the MTD apply. There will be no further dose escalation at this point, and the MTD will be the dose level at which no more than 1/6 subjects experience a DLT. Once 6 patients have been treated at the MTD, an additional 10 patients will be treated at that dose level to further delineate toxicity and efficacy at that dose level.