Inclusion Criteria:

1. Confirmed diagnosis of CLL or SLL:

2. No prior therapy for CLL, including treatment for autoimmune conditions that have
developed since the initial diagnosis of CLL.

3. Active disease requiring therapy:

1. Evidence of progressive marrow failure as manifested by the development of
worsening of anemia and / or thrombocytopenia

2. Massive, progressive, or symptomatic splenomegaly

3. Massive, progressive, or symptomatic lymphadenopathy

4. Progressive lymphocytosis with an increase of more than 50% over a 2-month
period or a lymphocyte doubling time of less than 6 months.

5. Autoimmune anemia and/or thrombocytopenia poorly responsive to corticosteroids
or other standard therapy

6. Presence of disease related symptoms: unintentional weight loss of more than 10%
within previous 6 months, significant fatigue, fevers greater than 100.5 F or
38.0 C for 2 or more weeks without evidence of infection, night sweats > 1 month
without evidence of infection.

4. Understand and voluntarily sign an informed consent form.

5. Age > = 18 years at the time of signing the informed consent form.

6. Able to adhere to the study visit schedule and other protocol requirements.

7. ECOG performance status of < = 2 at study entry

8. Labs within these ranges:

- ANC > = 1000/mm³

- Platelets > = 50,000/mm³

- Creatinine clearance of ≥ 30 mL/min by Cockcroft-Gault formula.

- Total bilirubin < = 1.5 x the ULN

- AST (SGOT) and ALT (SGPT) < = 3 x ULN (or < = 5 x ULN if due to the CLL)

9. Disease free of prior malignancies for > = 2 years with exception of curatively
treated basal cell carcinoma, squamous cell carcinoma of the skin, or carcinoma "in
situ" of the cervix or breast.

10. All study participants must be registered into the mandatory S.T.E.P.S.® program,
and be willing and able to comply with the requirements of S.T.E.P.S.®

11. Females of childbearing potential (FCBP)† must have a negative pregnancy test within
10 - 14 days prior to and again within 24 hours of starting treatment and again
within 24 hours before the first dose of lenalidomide AND thalidomide. FCBP must
either commit to continued abstinence from heterosexual intercourse or begin TWO
acceptable methods of birth control, one highly effective method and one additional
effective method AT THE SAME TIME, at least 28 days before she starts taking
lenalidomide and/or thalidomide. FCBP must also agree to ongoing pregnancy testing.
Men must agree to use a latex condom during sexual contact with a FCBP even if they
have had a successful vasectomy.

12. Able to take aspirin 81 or 325 mg daily as prophylactic anticoagulation, unless
already on therapeutic anticoagulation.

Exclusion Criteria:

1. Any serious medical condition, laboratory abnormality, or psychiatric illness that
would prevent the subject from providing informed consent.

2. Any condition, including the presence of laboratory abnormalities, which places the
subject at unacceptable risk if he/she were to participate in the study or confounds
the ability to interpret data from the study.

3. Evidence of laboratory TLS by Cairo-Bishop Definition of Tumor Lysis Syndrome.
Subjects may be enrolled upon correction of electrolyte abnormalities.

4. Concurrent use of other anti-cancer agents or treatments.

5. Prior treatment with thalidomide or lenalidomide.

6. Active serious infection not controlled with antibiotics.

7. Autoimmune hemolytic anemia or thrombocytopenia requiring treatment.

8. Known positive for HIV

9. Active infection with hepatitis B, defined by being positive for HepBsAg or Hep B DNA
by PCR, or hepatitis C

10. Pre-existing peripheral neuropathy > = grade 2

11. Pregnant or breast feeding females.