X-ray computed tomography (CT) has emerged as a key imaging tool in the characterization of materials, allowing three-dimensional visualization of an object non-destructively as well as enabling the monitoring of damage accumulation over time through time-lapse imaging. However, small defects and cracks can be difficult to detect, particularly in composite materials where low-contrast, plate-like geometries of large area can compromise detectability. Here, we investigate a number of strategies aimed at increasing the capability of X-ray CT to detect composite damage such as transverse ply cracking and delamination, looking specifically at a woven glass fibre-reinforced three-dimensional composite. High-resolution region of interest (ROI) scanning, in situ loading, phase contrast and contrast agents are examined systematically as strategies for improving the defect detectability. Spatial resolution, contrast, signal-to-noise ratio, full width at half maximum, user friendliness and measurement time are all considered. Taken together, the results suggest that high-resolution ROI scanning combined with the increased contrast resulting from staining give the highest defect detectability.