Inclusion Criteria:

- Voluntary written informed consent before performance of any study-related procedure
not part of normal medical care, with the understanding that consent may be withdrawn
by the subject at any time without prejudice to future medical care

- Female subjects who:

- Are postmenopausal for at least 1 year before the screening visit, OR

- Are surgically sterile, OR

- If they are of childbearing potential, agree to practice 2 effective methods of
contraception, at the same time, from the time of signing the informed consent
form through 30 days after the last dose of bortezomib, or agree to completely
abstain from heterosexual intercourse

- Male subjects, even if surgically sterilized (i.e., status post vasectomy) who:

- Agree to practice effective barrier contraception during the entire study
treatment period and through a minimum of 30 days after the last dose of study
drug, OR

- Agree to completely abstain from heterosexual intercourse

- The patient has relapsed or refractory B or T cell acute lymphoblastic leukemia that
has progressed following at least one prior therapy; Philadelphia chromosome-positive
(Ph+) patients are eligible; relapsed ALL is defined in patients as the reappearance
of leukemia cells in the peripheral blood or bone marrow after a complete remission;
refractory ALL is defined in patients as failure to achieve a complete remission
after induction therapy; complete remission is defined by < 5% leukemia cells in the
bone marrow with recovery of peripheral blood counts; relapsed disease can be
documented by bone marrow biopsy (> 5% cells in the bone marrow) or by flow cytometry
in the peripheral blood

- Must have received at least one (1) line of prior systemic therapy that may NOT have
included VELCADE (bortezomib); patients who have undergone autologous/allogeneic stem
cell transplantation are eligible

- Transplant eligible patients are eligible

- Eastern Cooperative Oncology Group (ECOG) performance status 0-2

- No poorly controlled intercurrent illness including, but not limited to, ongoing or
active infection, poorly controlled diabetes, symptomatic congestive heart failure,
or psychiatric illness that in the opinion of the investigator would limit compliance
with study requirements

- Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) < 2.5 x upper
limit of normal

- Total bilirubin =< 1.5 x upper limit of normal (ULN) unless elevation is due to
leukemia infiltration as defined by characteristic radiographic appearance or liver
biopsy

- Patients must have adequate renal function defined as creatinine clearance of 30
ml/minute (Cockcroft-Gault)

Exclusion Criteria:

- Patient has > 1.5 x ULN total bilirubin

- Patient has >= grade 2 peripheral neuropathy

- 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
electrocardiogram (ECG) abnormality at screening must be documented by the
investigator as not medically relevant

- Patient has hypersensitivity to bortezomib, boron, or mannitol

- Female subject is pregnant or lactating

- Serious medical or psychiatric illness likely to interfere with participation in this
clinical study

- Diagnosed or treated for 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

- Participation in clinical trials with other investigational agents not included in
this trial throughout the duration of this trial

- 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

- The patient has been exposed to >= 350mg/m^2 of anthracycline (doxorubicin
equivalent)

- The patient has a left ventricular ejection fraction of < 40%