High resolution images in PET based on small individual detectors are obtained at the cost of low sensitivity and increased detector scatter. These limitations can be partially overcome by enlarging discrimination windows to include more low-energy events and by developing more efficient energy-dependent methods to correct for scatter radiation from all sources. The feasibility of multispectral scatter correction was assessed by decomposing response functions acquired in multiple energy windows into four basic components: object, collimator and detector scatter, and trues. The shape and intensity of these components are different and energy-dependent. They are shown to contribute to image formation in three ways: useful (true), potentially useful (detector scatter), and undesirable (object and collimator scatter) information to the image over the entire energy range. With the Sherbrooke animal PET system, restoration of detector scatter in every energy window would allow nearly 90% of all detected events to participate in image formation. These observations suggest that multispectral acquisition is a promising solution for increasing sensitivity in high resolution PET. This can be achieved without loss of image quality if energy-dependent methods are made available to preserve useful events as potentially useful events are restored and undesirable events removed.