Due to round-off errors, watermark detection may not be perfect in the absence of attacks. In this paper, watermarks are adjusted so that the watermarked image is integer-valued. Near-perfect detection is achieved by the DC components of DCT and approximation images. Perfect detection is achieved by full-band watermarking. Although the adjusted watermark is image-dependant, it need not be stored in a watermark bank, as it can be generated from an original watermark and a host image. In this paper, the DC components of discrete cosine transform (DCT) and discrete Hadamard transform (DHT) are shown to be able to attain near-perfect detection, while perfect detection is achieved by full-band watermarking. Time-domain watermarking is not band-limited and hence is equivalent to full-band watermarking.