Pre-neutropenic fever (PNF) (fever following chemotherapy but before developing low white cells) and neutropenic fever (NF) (fever in the setting of low white cells) are very common after chemotherapy for acute leukemia, bone marrow transplantation or Chimeric Antigen Receptor T-cell (CAR T) therapy. Often, there is no bacterial cause for fever found, and in the setting of a well patient with resolved fever, some studies have shown it to be safe to cease antibiotic therapy which was commenced at the onset of fever. This reduces the overall exposure to antibiotics, which can be beneficial to the patient (reduced risk of resistant bugs emerging, reduced serious side effects). However, some subgroups of high-risk patients have been underrepresented in these studies (in particular, those who have received a bone marrow transplant from a donor, those with longer duration of low white cells) and none have been performed in Australia, hence applying this data to our setting and patient groups is indirect and further data are needed. This study plans to recruit participants who have received chemotherapy for acute leukemia or a stem cell transplant (either their own cells or a donor's cells) or CAR T-cell therapy and perform a trial to compare early stopping of antibiotics (STOP arm) to the standard of care, which traditionally involves continuing antibiotics until the white cell count reaches above a specific threshold. The primary study outcome is duration of days free of antibiotics within 28 days of study allocation. The investigators will also observe for important clinical outcomes including rates of fever recurrence, bloodstream and other infections, intensive care admission and mortality. Patients will stay in hospital during this period, even in the setting of stopping antibiotics, and these antibiotics can be recommenced urgently according to the sepsis protocol if there is concern for infection.