This paper comes to fill a gap in watermarking theory, analyzing the exact performance of the scalar Costa scheme (SCS) facing additive Gaussian attacks when the usual approximation of high-resolution quantization is not valid, thus taking into account the host statistics. The analysis is focused on the assessment of the probability of error, showing new results, an although it is valid in a general scenario, its practical interest is increased when SCS is used in conjunction with the so-called spread-transform. The accomplished reformulation of the problem also permits to show that the achievable rate of SCS is never worse than that of classical spread-spectrum-based methods, as it was thought so far, and allows to establish interesting links with spread spectrum and the Improved Spread Spectrum method.