The principle of using ultrasonic computed tomography (UCT) clinically for mapping tissue acoustic properties was suggested almost 40 years ago. Despite strong research activity, UCT been unable to rival its x-ray counterpart in terms of the ability to distinguish tissue pathologies. Conventional piezoelectric detectors deployed in UCT are termed phase-sensitive (PS) and it is well established that this property can lead to artefacts related to refraction and phase-cancellation that mask true tissue structure, particularly for reconstructions involving attenuation. Equally, it has long been known that phase-insensitive (PI) detectors are more immune to this effect, although sufficiently sensitive devices for clinical use have not been available. This paper explores the application of novel PI detectors to UCT. Their operating principle is based on exploiting the pyroelectric properties of the piezoelectric polymer polyvinylidene difluoride. An important detector performance characteristic which makes it particularly suited to UCT, is the lack of directionality of the PI response, relative to the PS detector mode of operation. The performance of the detectors is compared to conventional PS detection methods, for quantitatively assessing the attenuation distribution within various test objects, including a two-phase polyurethane phantom. UCT images are presented for a range of single detector apertures; tomographic reconstruction images being compared with the known structure of phantoms containing inserts as small as 3 mm, which were readily imaged. For larger diameter inserts (>10 mm), the transmitter-detector combination was able to establish the attenuation coefficient of the insert to within ±10% of values determined separately from plane-wave measurements on representative material plaques. The research has demonstrated that the new PI detectors are significantly less susceptible to refraction and phase-cancellation artefacts, generating realistic images in situations where conventionally-employed through-transmission PS detection techniques were unable to do so. The implications of the study to the potential screening of breast disease are discussed.