The goal of this clinical research study is to find the highest tolerable dose of 4'-thio-araC (thiarabine) that can be given to patients with advanced blood cancer. The safety of this drug will also be studied and 2 different dose schedules will be tested.

The Study Drug:

Thiarabine is designed to damage and destroy the DNA of cancer cells. This may cause the cells to die.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to 1 of 2 study groups based on when you joined the study. The first set of 3 participants will be enrolled in Group 1, and the 2nd set of 3 participants will be enrolled in Group 2. The 3rd set of 3 participants will be enrolled in Group 1, then the 4th set of 3 participants in Group 2, and so on until all participants are enrolled.

• Group 1 will receive thiarabine for 3 days in a row in each cycle.
• Group 2 will receive thiarabine for 5 days a row in each cycle.

Cycles in this study are 3-6 weeks long, depending on how you are doing. You may begin a new cycle when your blood cell counts have returned to an appropriate level. However, you may begin a new study cycle earlier than that if the disease gets worse or does not improve.

The dose of thiarabine you receive will depend on when you joined this study. The first set of participants will receive the lowest dose level of thiarabine. Each new set will receive a higher dose of thiarabine than the set before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of thiarabine is found.

Study Drug Administration:

You will receive thiarabine by vein over about 1 hour (+/- 15 minutes) on Days 1-3 (Group 1) or Days 1-5 (Group 2) of each cycle.

Study Visits:

Blood (about 2 tablespoons) will be drawn for routine tests 1 or 2 times a week. If the disease responds well, the study doctor may decide these blood tests will occur less often.

At every study visit, you will be asked about any drugs you may be taking and symptoms you may be having.

You will have an ECG within 2 days before each cycle.

At any time the doctor thinks it is needed, you will have a bone marrow aspiration to check the status of the disease.

Length of Participation:

You may continue taking the study drug for as long as the doctor thinks it is in your best interest. You will be taken off study early if intolerable side effects occur. You may be taken off study early if the disease gets worse.

Follow-Up:

At 30 days after your last study drug dose, you will be asked about any side effects you may be having. This may be done during a regular clinic visit or by phone call from the study doctor or staff.

This is an investigational study. Thiarabine is not FDA approved or commercially available. It is currently being used for research purposes only.

Up to 70 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients must have relapsed/refractory leukemias for which no standard therapies are anticipated to result in a durable remission. Patients with poor-risk myelodysplasia (MDS) [i.e. refractory anemia with excess blasts (RAEB-1 or RAEB-2) by WHO classification] and chronic myelomonocytic leukemia (CMML) are also candidates for this protocol. Relapsed/refractory leukemias include acute non-lymphocytic leukemia (AML) by WHO classification, acute lymphocytic leukemia (ALL), chronic lymphocytic leukemia (CLL), or chronic myelogenous leukemia (CML) in blast crisis.
2. Patients with refractory/relapsed leukemia 16 years or older are eligible. Patients 60 years or older with newly diagnosed AML are eligible if they are not candidates for, or if they refuse, intensive chemotherapy.
3. Eastern Cooperative Oncology Group (ECOG) performance status of 0-3.
4. Women of child-bearing potential (ie, a woman who has not been postmenopausal for at least 12 consecutive months or who had not undergone previous surgical sterilization) must use acceptable contraceptive methods (abstinence, intrauterine device (IUD), oral contraceptive or double barrier device), and must have a negative urine pregnancy test within 2 weeks prior to beginning treatment on this trial. Nursing patients are excluded. Sexually active men must also use acceptable contraceptive methods for the duration of time on study.
5. Continued from #4: Pregnant and nursing patients are excluded because the effects of 4'-thio-araC on a fetus or nursing child are unknown.
6. Must be able and willing to give written informed consent
7. In the absence of rapidly progressing disease, the interval from prior treatment to time of study drug administration should be at least 2 weeks for cytotoxic agents or at least 5 half-lives for noncytotoxic agents. If the patient is on hydroxyurea to control peripheral blood leukemic cell counts, the patient must be off hydroxyurea for at least 24 hours before initiation of treatment on this protocol. Persistent clinically significant toxicities from prior chemotherapy must not be greater than grade 1.
8. Patients must have the following clinical laboratory values unless considered due to leukemic organ involvement: 1. Serum creatinine </= 1.3 mg/dl or creatinine clearance > 40 ml/min. 2. Total bilirubin </= 1.5* the upper limit of normal unless considered due to Gilbert's syndrome. 3. Alanine aminotransferase (ALT), or aspartate aminotransferase (AST) </= 3* the upper limit of normal unless considered due to organ leukemic involvement.
9. Patients with active central nervous system (CNS) involvement of leukemia disease are included and will be treated concurrently with intrathecal therapy.

Exclusion Criteria:

1. Uncontrolled intercurrent illness including, but not limited to uncontrolled infection (e.g. requiring IV antibiotics, etc), symptomatic congestive heart failure, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
2. Active heart disease including myocardial infarction within previous 3 months, symptomatic coronary artery disease, corrected QT interval (QTc) > 480, arrhythmias not controlled by medication, or uncontrolled congestive heart failure defined as Class II to IV per New York Heart Association Classification.
3. Patients receiving any other standard or investigational treatment for their hematologic malignancy.
4. Patients with known HIV positive disease; patients with active hepatitis.