Note: G-CSF and platelet transfusions cannot be used to increase counts to meet eligibility criteria Platelet count >= 50,000/mm^3; note: platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment NOTE: platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before registration Platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Obtained =< 21 days prior to registration and confirmed prior to the first dose of study drug: Platelets (PLT) >= 75,000/uL; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Absolute neutrophil count (ANC) >= 1,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment; patients may receive growth factor support prior to initiating therapy but must remain off of growth factor for at least 7 days before starting therapy and must meet eligibility on cycle 1, day 1; patients who complete the consent process but do not meet hematologic eligibility within 30 days may be re-consented and enrolled on study if they ultimately do meet eligibility requirements before day +180; no patients may initiate therapy after day +180 and they must meet all remaining eligibility criteria Platelet count >= 75,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Absolute neutrophil count (ANC) ? 1,000/mm^3 without growth factor support and platelet count ? 75,000/mm^3. Platelet transfusions to help participants meet eligibility criteria are not allowed within 3 days before randomization. Platelet count >= 75,000/mm^3. Platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet count >= 75,000/mcL; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Transfusions are not allowed to meet eligibility criteria Platelet count >= 75,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 7 days before study enrollment Platelet count of < 100 x 10^9/L; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet count >= 100,000/mm^3 or >= 75,000/mm^3 if thrombocytopenia is attributed to B-NHL (involvement of bone marrow or due to splenomegaly or immune thrombocytopenic purpura); platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet count >= 75 mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 7 days before study enrollment Obtained ? 14 days prior to registration: platelet count ? 75,000/mm^3 (NOTE: platelet transfusions in order to help patients meet eligibility criteria are not allowed) Platelet count >= 75,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelets (PLT) >= 50,000/uL; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment, obtained =< 21 days prior to registration and confirmed prior to the first dose of study drug Platelets >= 75 K/uL (platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment) Platelet count >= 75,000/mm^3; platelet transfusions are not allowed within 3 days before study enrollment Platelet count >= 75,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Absolute neutrophil count (ANC) ? 1,000 per cubic milliliter (/mm^3) and platelet count ? 75,000/mm^3. Platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before randomization. Platelet count >= 100,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Absolute neutrophil count (ANC) ? 1000/mm^3 and platelet count ? 75,000/mm^3. Platelet transfusions to help participants meet eligibility criteria were not allowed within 3 days prior to randomization. Platelet count >= 75 x 10^9/L; platelet support is permitted within 14 days although platelet transfusions to help participants meet eligibility criteria are not allowed within 72 hours (3 days) prior to the blood sample to confirm protocol eligibility, within 14 days prior to registration Platelet or red cell transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet count >= 50,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet count >= 75,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days prior to screening complete blood count (CBC) or cycle 1, day 1 treatment Platelet count >= 75,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Hemoglobin > 8.0 g/dL; red blood cell transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment Platelet count >= 50/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 7 days before study enrollment Platelet count >= 100,000/mm^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment