Inclusion Criteria:

          -  For phase I, patients can be HMA-naive high-risk MDS (Int-2 or high risk by the
             International Prognostic Scoring System [IPSS] with overall score >= 1.5) with excess
             blasts > 5%, or relapsed/refractory MDS post-HMA failure (defined as prior receipt of
             4 cycles of HMA therapy with failure to attain a response, or progression of disease
             or relapse at any time after prior response to HMA therapy) with > 5% blasts

          -  For phase II, patients will be divided into 2 cohorts: Cohort A: patients with
             HMA-naive high-risk MDS (Int-2 or high risk by the IPSS with overall score >= 1.5)
             with excess blasts > 5%. Cohort B: patients with relapsed/refractory MDS post-HMA
             failure (defined as prior receipt of 4 cycles of HMA therapy with failure to attain a
             response, or progression of disease or relapse at any time after prior response to HMA
             therapy) with > 5% blasts are eligible. Note: Patients with chronic myelomonocytic
             leukemia (CMML) and therapy-related MDS are eligible. Hydroxyurea is allowed to lower
             the white cell count =< 10,000/ul prior to initiation of venetoclax

          -  Total bilirubin < 3 x upper limit of normal (ULN) unless increase is due to Gilbert's
             disease or leukemic involvement

          -  Alanine aminotransferase (ALT) < 4 x ULN unless considered due to leukemic involvement

          -  Creatinine < 2 x ULN unless related to the disease

          -  Signed written informed consent

          -  Females must be surgically or biologically sterile or postmenopausal (amenorrheic for
             at least 12 months) or if of childbearing potential, must have a negative serum or
             urine pregnancy test within 72 hours before the start of the treatment. Women of
             childbearing potential must agree to use an adequate method of contraception during
             the study and until 3 months after the last treatment

          -  Males must be surgically or biologically sterile or agree to use an adequate method of
             contraception during the study until 3 months after the last treatment

        Exclusion Criteria:

          -  Patients having received any prior BCL2 inhibitor therapy

          -  Patients with MDS with IPSS risk categories low or Int-1 (overall IPSS score < 1.5)

          -  Pregnant or breastfeeding