The ECAT EXACT3D (CTI/Siemens 966) 3D-only PET tomograph has unprecedented sensitivity due to the large BGO (bismuth germanate) detector volume. However, the consequences of a large (23.4 cm) axial field-of-view (FOV) and the need for a patient port diameter to accommodate body scanning make the device more sensitive to photons arising from activity outside the direct (coincidence) FOV. This leads to relatively higher deadtime and an increased registration of random and scatter (true) coincidences. The purpose of this study is to determine the influence of activity outside the FOV on (i) noise-equivalent counts (NEC) and (ii) the performance of a 'model-based' scatter correction algorithm, and to investigate the effect of side shielding additional to that supplied with the tomograph. Annular shielding designed for brain scanning increased the NEC for blood flow (H[2]15O) measurement (integrated over 120 s) by up to 25%. For 11C tracer studies, the increase is less than 5% over 120 min. Purpose-built additional body shielding, made to conform to the shape of a volunteer, reduced the randoms count rate in a heart blood flow measurement (H[2]15O) by about 30%. After scatter correction the discrepancy between ROI count ratios for compartments within the 20 cm diameter 'Utah' phantom differed by less than 5% from true (sampled) activity concentration ratios. This was so with or without activity outside the FOV and with or without additional side shielding. Count rate performance is thus improved by extra shielding but more improvement is seen in head than in body scanning. Measurement of heart blood flow using bolus injections of H(2)15O would benefit from the use of detectors with lower deadtime and superior timing resolution such as LSO (lutetium oxyorthosilicate).