Eligible patients will receive bendamustine as 4 courses of 70 mg/m2 on days 1 and 2 every 28 days and 30 mg alemtuzumab s.c. continuously on days 1, 3 and 5 of every week, for a maximum of 16 weeks. Safety assessments will be conducted weekly; efficacy assessments including imaging will be performed at months 2, 4, 6, 10 and 16. Bone marrow biopsies will be performed upon CR (according to the 2008 IWCLL response criteria) or fixed at 6 and 16 months.