To further enhance the security of the present digital watermarking, the reversibility of widely researched adaptive watermarking is investigated. First, watermarking schemes are classified and generalized. Then, on the assumption that adaptive watermarking places no constraint on the formation of watermarks and scaling factors, the reversibility and quasi-reversibility, together with their resulting reverse and quasi-reverse engineering attacks, which could disturb or even overturn the ownership verification, are defined, analyzed and illustrated. Finally, the necessity of placing constraints on the formation of watermarks and scaling factors is concluded, and the essential irreversibility of some adaptive technologies, which can be used to enhance the security, is pointed out. Making watermarks and scaling factors one-way dependent on original data, and exploiting the human perceptual system, help watermarking become resistant to the above attacks and more reliable in ownership verification.