Increasingly widespread communication of medical images across multiple user systems raises concerns for image security, for which digital image watermarking offers one solution. While digital image watermarking methods have been widely studied, much less attention has been paid to their application in medical imaging situations, due partially to speculations on loss in viewer performance due to degradation of image information. Such concerns are addressed if the amount of information lost due to watermarking can be kept at minimal levels and certainly well below visual perception thresholds. This paper describes a method for applying watermarks to medical images on a locally varying basis, so as to ensure that the visual impact of changes in pixel values is minimal. The method uses an adaptive approach based on 8x8 blocks of pixels, and takes into account the imaging modality and local image contents according to common perceptual information models, when determining the amount of watermark payload information to be encoded. It is assumed that "light" watermarking is desirable, and some typical examples of watermarks that might be used (e.g. patient identifiers and examination details) are provided to substantiate this position. Experimental results for typical CT and MR images are presented, and the performance of the method across a range of different choices of parameters is analysed. This would be useful in situations where images are manipulated on and transferred between many different independent image storage systems (including PACS), which would not allow the integrity of the image data to be assured.