Sound applications based on sinusoidal modeling highly depend on the efficiency and the precision of the estimators of its analysis stage. In a previous work, theoretical bounds for the best achievable precision were shown and these bounds are reached by efficient estimators like the reassignment or the derivative methods. We show that it is possible to break these theoretical bounds with just a few additional bits of information of the original content, introducing the concept of “informed analysis”. This paper shows that existing estimators combined with some additional information can reach any expected level of precision, even in very low signal-to-noise ratio conditions, thus enabling high-quality sound effects, without the typical but unwanted musical noise.