Inclusion Criteria:

          -  Diagnosis of one of the following:

               -  Previously untreated Ph-positive ALL (either t[9;22] and/or bcr-abl positive)
                  (includes patients initiated on first course of hyper-CVAD before cytogenetics
                  known) or with lymphoid accelerated or blast phase chronic myelogenous leukemia
                  (CML)

               -  Previously treated Ph-positive ALL or CML (in accelerated phase or blast phase),
                  after 1-2 courses of chemotherapy with or without other tyrosine kinase
                  inhibitors (TKIs)

                    -  If they achieved complete response (CR), they are assessable only for
                       event-free and overall survival, or

                    -  If they failed to achieve CR, they are assessable for CR, event-free, and
                       overall survival

          -  Performance status =< 2 (Eastern Cooperative Oncology Group [ECOG] scale)

          -  Total serum bilirubin =< 1.5 x upper limit of normal (ULN), unless due to Gilbert's
             syndrome

          -  Alanine aminotransferase (ALT) =< 2 x ULN

          -  Aspartate aminotransferase (AST) =< 2.5 x ULN

          -  Serum lipase and amylase =< 1.5 x ULN

          -  For females of childbearing potential, a negative pregnancy test must be documented
             prior to randomization

          -  Female and male patients who are fertile must agree to use an effective form of
             contraception with their sexual partners from randomization through 4 months after the
             end of treatment

          -  Adequate cardiac function as assessed clinically by history and physical examination

          -  Signed informed consent

        Exclusion Criteria:

          -  Active serious infection not controlled by oral or intravenous antibiotics

          -  Known active hepatitis B; patients with chronic hepatitis B who are on appropriate
             viral suppressive therapy may be allowed after discussion with the principal
             investigator (PI)

          -  History of acute pancreatitis within 1 year of study or history of chronic
             pancreatitis

          -  History of alcohol abuse

          -  Uncontrolled hypertriglyceridemia (triglycerides > 450 mg/dL)

          -  Active secondary malignancy other than skin cancer (e.g., basal cell carcinoma or
             squamous cell carcinoma) that in the investigator's opinion will shorten survival to
             less than 1 year

          -  Active grade III-V cardiac failure as defined by the New York Heart Association
             criteria

          -  Clinically significant, uncontrolled, or active cardiovascular disease, specifically
             including, but not restricted to:

               -  Any history of myocardial infarction (MI), stroke, or revascularization

               -  Unstable angina or transient ischemic attack prior to enrollment

               -  Congestive heart failure prior to enrollment, or left ventricular ejection
                  fraction (LVEF) less than lower limit of normal per local institutional standards
                  prior to enrollment

               -  Diagnosed or suspected congenital long QT syndrome

               -  Any history of clinically significant atrial or ventricular arrhythmias (such as
                  atrial fibrillation, ventricular tachycardia, ventricular fibrillation, or
                  torsades de pointes) as determined by the treating physician

               -  Prolonged corrected QT (QTc) interval on pre-entry electrocardiogram (> 470 msec)
                  unless corrected after electrolyte replacement

               -  Any history of venous thromboembolism including deep venous thrombosis or
                  pulmonary embolism

               -  Uncontrolled hypertension (diastolic blood pressure > 90 mmHg; systolic > 140
                  mmHg); patients with hypertension should be under treatment on study entry to
                  effect blood pressure control

          -  Patients currently taking drugs that are generally accepted to have a risk of causing
             torsades de pointes (unless these can be changed to acceptable alternatives)

          -  Taking any medications or herbal supplements that are known to be strong inhibitors of
             cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) within at least 14 days
             before the first dose of ponatinib

          -  Prior history of treatment with ponatinibfor > 1 month; patient who has been treated
             with ponatinib for 1 month prior starting the treatment is eligible

          -  Treatment with any investigational antileukemic agents or chemotherapy agents in the
             last 7 days before study entry, unless full recovery from side effects has occurred or
             patient has rapidly progressive disease judged to be life-threatening by the
             investigator; patient who has been treated with ponatinib for 1 month prior starting
             the treatment is eligible

          -  Pregnant and lactating women will not be eligible; women of childbearing potential
             should have a negative pregnancy test prior to entering on the study and be willing to
             practice methods of contraception; women do not have childbearing potential if they
             have had a hysterectomy or are postmenopausal without menses for 12 months; in
             addition, men enrolled on this study should understand the risks to any sexual partner
             of childbearing potential and should practice an effective method of birth control

          -  History of significant bleeding disorder unrelated to cancer, including:

               -  Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease)

               -  Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor
                  VIII antibodies)

          -  Patients with documented significant pleural or pericardial effusions unless they are
             thought to be secondary to their leukemia