Inclusion Criteria:

- ECOG 0-2 OR Karnofsky 60-100%

- Platelet count >= 100,000/mm^3

- Absolute neutrophil count >= 1,500/mm^3

- WBC >= 3,000/mm^3

- AST and ALT =< 2.5 times upper limit of normal

- Bilirubin normal

- No symptomatic congestive heart failure

- Creatinine normal OR creatinine clearance >= 60 mL/min

- No unstable angina pectoris

- No cardiac arrhythmia

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No other malignancy within the past 5 years except basal cell skin cancer or
carcinoma in situ of the cervix

- No ongoing or active infection

- No psychiatric illness or social situation that would preclude study compliance

- No other uncontrolled illness

- At least 4 weeks since prior chemotherapy

- No more than 2 prior chemotherapy regimens

- At least 6 months since prior external beam radiotherapy for locoregional disease in
the thyroid bed or to the cervical or upper mediastinal lymph nodes (dose =< 6,000
cGy)

- At least 6 months since prior radioiodine therapy

- No prior external radiotherapy to the measured tumor

- Prior thyroidectomy allowed

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No other concurrent investigational agents

- No other concurrent anticancer therapy

- Unresponsive to prior radioiodine therapy

- Histologically confirmed differentiated thyroid cancer-papillary or follicular type,
including, but not limited to, any of the following variants: hurthle cell
(oxyphilic), insular, columnar cell, tall cell

- Metastatic disease

- At least 1 unidimensionally measurable lesion >= 20 mm by conventional techniques OR
>= 10 mm by spiral CT scan

- No prior radiotherapy to the only measurable lesion

- No radioiodine uptake in the measured metastatic tumor by radioiodine scan (Note:
Must have had >= 1 radioiodine scan since the last radioiodine treatment)

- No known brain metastases