Inclusion Criteria:

- Histological confirmation of follicular, papillary, insular, or Hürthle-cell thyroid
carcinoma. Histologic slides and/or tissue blocks must be reviewed at the University
of Kentucky Medical Center.

- Patients must have an unresectable, distantly metastatic tumor, which does not
concentrate radioactive iodine. Alternatively, follicular or papillary thyroid
carcinoma patients with large distant tumor burdens which have not sufficiently
responded to more than 800 mCi I-131 cumulative therapy and are progressive (criteria
#4) may be appropriate for inclusion.

- No systemic chemotherapy agents within 4 weeks of initiation of therapy.

- Patients must have 3 consecutive radiographic evaluations demonstrating a cumulative
30% increase in tumor volume over a period of one year or less.

- Patients must be over the age of 18 years with the ability to understand and willing
to sign an informed consent.

- Non-pregnant (if female). Women of childbearing potential (fertile females) must have
a negative serum or urine pregnancy test within one day of starting study drug. In
addition, sexually active fertile female subjects must agree to adequate
contraceptive methods (oral, injectable, or implantable hormonal contraceptive; tubal
ligation, intrauterine device, barrier contraceptive with spermicide; or vasectomized
partner) while on study drug. Men must agree to use latex condoms when having sex
with fertile women.

- Karnofsky performance status ≥ 70.

- Baseline laboratory studies:

- absolute neutrophil count (ANC) > 1000/mm3

- platelet count ≥ 100 K/mm3

- creatinine ≤ 1.5 mg/dL, and

- transaminase levels (AST/SGOT, ALT/SGPT) ≤ 2 x upper limit of normal (ULN) (or ≤
5 x I:M if hepatic metastases are present)

- Disease free of other prior malignancies for ≥ 5 years, with the exception of
currently treated basal cell/squamous cell carcinoma of the skin or "in-situ"
carcinoma of the cervix or breast.

- Thyroid stimulating hormone (TSH, thyrotropin) levels must be suppressed with
sufficient levothyroxine to be kept beneath the normal range of the assay.

Exclusion Criteria:

- Patients may not have had prior REVLIMID® therapy.

- No serious concomitant medical or psychiatric illness that might interfere with
informed consent or conduct of the study, including active infections that are not
controlled with medication.

- Patients must not be pregnant or breastfeeding.

- Use of any other experimental drug or therapy within 28 days of baseline.

- Known hypersensitivity to thalidomide.

- The development of erythema nodosum, characterized by a desquamating rash, while
taking thalidomide or similar drugs.

- 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.

- Concurrent use of other anti-cancer agents or treatments, with the exception of
thyrotropin-suppression by levothyroxine.

- All subjects with central nervous system involvement, with the exception of those
subjects whose central nervous system metastases have been treated with either
radiotherapy and/or surgery and remain asymptomatic with no evidence of active
central nervous system disease (verified by computed tomography [CT] scan or magnetic
resonance imaging [MRI]) for at least 6 months.

- Known to be positive for HIV or infectious hepatitis, type A, B, or C.

- Patients with medullary or anaplastic thyroid carcinomas are excluded. Patients
whose disease is limited to bone metastases are excluded.