The goal of this clinical research study is to learn if bortezomib can help to control MDS. The safety of this drug will also be studied.

Bortezomib is designed to block a protein that causes cells to grow. This may cause cancer cells to die.

Study Drug Administration:

If you are found to be eligible to take part in this study, you will receive bortezomib as an injection under the skin on Days 1, 4, 8, and 11 of each 21-day cycle.

Study Visits:

At each visit, you will be asked about any drugs you may be taking and any side effects you may be having.

One (1) time a week during Cycle 1, blood (about 2 tablespoons) will be drawn for routine tests.

On Day 21 of Cycles 1 and 3, you will have a bone marrow aspiration and/or biopsy to check the status of the disease and for cytogenetic testing.

On Day 1 of Cycles 2 and beyond, blood (about 2 tablespoons) will be drawn for routine tests.

If your doctor thinks it is needed, you may have additional bone aspirations and/or biopsies to check the status of the disease and/or for cytogenetic testing.

Length of Treatment:

You may continue taking the study drug for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, if you are able to have an allogeneic stem cell transplant (a stem cell transplant from a donor), or if you are unable to follow study directions.

Your participation on the study will be over once you have completed the end-of- treatment visit.

End-of-Treatment Visit:

At 30 days after your last dose of study drug:

• You will be asked about any drugs you may be taking and any side effects you may have had.
• Blood (about 2 tablespoons) will be drawn for routine tests.
• If your doctor thinks it is needed, you will have a bone marrow aspirate and/or biopsy to check the status of the disease and for cytogenetic testing.

This is an investigational study. Bortezomib is FDA approved and commercially available to treat multiple myeloma and mantle cell lymphoma. Giving it to patients with MDS is investigational.

Up to 40 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Voluntary signed informed consent before performance of any study-related procedure not part of normal medical care, indicating that that the patient is aware of the investigational nature of the study in keeping with the policies of MD Anderson Cancer Center (MDACC) and with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care.
2. Presence of phosphorylated p65 NF-kB component in at least 5% of bone marrow cells
3. Age >/= 18 years of age at time of signing consent
4. Confirmed MDS by bone marrow biopsy according to World Health Organization (WHO) or French-American-British (FAB) criteria.
5. Classification by the International Prognostic Score System (IPSS) as low or intermediate-1 risk MDS according to cytogenetics, blood cytopenias and % bone marrow blasts within 28 days of the first dose of treatment in this study.
6. Patients must have received at least one prior therapy for MDS. Patients could have received transplant for MDS
7. Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0, 1 or 2.
8. Adequate liver function: Total bilirubin </= 1.5 × the upper limit of normal (ULN), unless presence of Gilbert's Syndrome. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) </= 2.5 × ULN or </= 5.0 ULN if hepatic involvement is present as determined by the investigator
9. Adequate renal function: Serum creatinine </= 2 mg/dL or a calculated creatinine clearance of >/= 50 mL/min (using the Cockcroft and Gault method).
10. Male patients, even if surgically sterilized (ie, status postvasectomy), who agree to practice effective barrier contraception during the entire study treatment period and through 30 days after the last dose of study treatment, or agree to completely abstain from heterosexual intercourse.
11. Female patients who are postmenopausal for at least 1 year before the Screening visit, or are surgically sterile, or if they are of childbearing potential, must have a negative pregnancy test within 72 hours of treatment start date and agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 30 days after the last dose of study treatment, OR agree to completely abstain from heterosexual intercourse
12. Willingness and ability to comply with scheduled visits, treatment plan, laboratory tests and other study procedures.

Exclusion Criteria:

1. Significant medical, psychiatric, cognitive or other conditions that may compromise the patient's ability to understand the patient information, to give informed consent, to comply with the study protocol, or to complete the study.
2. Any severe concurrent disease or condition (including active, uncontrolled systemic infection, symptomatic congestive heart failure, unstable angina pectoris or cardiac arrhythmia) that, in the judgment of the Investigator, would make the patient inappropriate for study participation.
3. Pregnant or lactating females.
4. Patient has >/= Grade 2 peripheral neuropathy
5. Patient had myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at screening must be documented by the investigator as not medically relevant.
6. Patient has hypersensitivity to bortezomib, boron, or mannitol
7. Current diagnosis of another malignancy within 2 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy.
8. Treatment with other investigational agents, chemotherapy, or immunotherapy within 14 days of the start of this trial and throughout the duration of this trial.
9. Radiation therapy within 3 weeks before randomization. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy.

2 years, 9 months