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It has recently been discovered that using pseudorandom sequences as carriers in spread-spectrum techniques for data-hiding is not at all a sufficient condition for ensuring data-hiding security. Using proper and realistic apriori hypothesis on the messages distribution, it is possible to accurately estimate the secret carriers by casting this estimation problem into a blind source separation problem. After reviewing relevant works on spread-spectrum security for watermarking, we further develop this topic to introduce the concept of security classes which broaden previous notions in watermarking security and fill the gap with steganography security as defined by Cachin. We define four security classes, namely, by order of creasing security: insecurity, key security, subspace security, and stegosecurity. To illustrate these views, we present two new modulations for truly secure watermarking in the watermark-only-attack (WOA) framework. The first one is called natural watermarking and can be made either stegosecure or subspace secure. The second is called circular watermarking and is key secure. We show that circular watermarking has robustness comparable to that of the insecure classical spread spectrum. We shall also propose information leakage measures to highlight the security level of our new spread-spectrum modulations.