The JPEG lossy compression technique in medical imagery has several disadvantages (at higher compression ratios), mainly due to block-distortion. We therefore investigated two methods, the lapped orthogonal transform (LOT) and the DCT/DST coder, for the use on medical image data. These techniques are block-based but they reduce the block- distortion by spreading it out over the entire image. These compression techniques were applied on four different types of medical images (MRI image, x-ray image, angiogram and CT- scan). They were then compared with results from JPEG and variable block size DCT coders. At a first stage, we determined the optimal block size for each image and for each technique. It was found that for a specific image, the optimal block size was independent of the different transform coders. For the x-ray image, the CT-scan and the angiogram an optimal block size of 32 by 32 was found, while for the MRI image the optimal block size was 16 by 16. Afterwards, for all images the rate-distortion curves of the different techniques were calculated, using the optimal block size. The overall conclusion from our experiments is that the LOT is the best transform among the ones being investigated for compressing medical images of many different kinds. However, JPEG should be used for very high image qualities, as it then requires almost the same bit rate as the LOT and as it requires fewer computations than the LOT technique.