The invention provides methods and related systems for embedding and detecting watermarks in images, such as JPEG or MPEG formatted images as well as other types of image signals. One method receives transform coefficients of the image, and changes the value of selected coefficients to embed watermark data in the coefficients. The changing of the coefficients is controlled such that it both embeds the data and forms an orientation signal that facilitates determination of rotation or scale of the image. Another aspect of the invention is a variation of embedding a watermark in an image. This method receives message bits to be embedded in the image, receives transform coefficients of the image, and maps the message bits to selected transform coefficients. The method changes the value of selected coefficients to embed data in the coefficients. The characteristics of the image are used to control the change of transform coefficients to embed the watermark, and a bit rate control is used to modify the change of transform coefficients to embed the watermark according to a bit rate limit.