The acceptance and uptake of the use of lossy compression for medical digital images depends on the reliable determination of limits on the loss of visual information, which would not adversely affect utility of the images for radiologists. A lack of widely accepted thresholds determining acceptable loss for various image modalities and for different compression techniques, motivates a need for further evidence of observer performance in such cases, via comparative studies. This paper contributes results of subjective testing for perceived image quality over three different image modality collections, using test sets of 5 images from each collection compressed by conventional lossy JPEG and by wavelet techniques at 4 different compression quality settings, presented independently to 4 radiologists for viewing. The results indicate a smooth decrease in perceived image quality in all three modalities when the compression quality setting was decreased, which implies there is some intrinsic difficulty in establishing a fixed ideal compression threshold within a modality. Furthermore, substantial differences were observed in the compression quality settings at which perceived absolute image quality was judged to be similar, across the three modalities. The results also indicate that the perceived image quality was usually slightly higher for wavelet compressed images than for JPEG compressed images, at a given compression quality setting.