As a rule in the 17th and 18th centuries musicians used to play not only the "written down" note, but extemporaneously added ornaments, arpeggios, and rhapsodic phrases. Because they themselves were composers, they also noted music just roughly, not in great detail. Therefore only in the course of playing, music emerged as it should be. But what exactly did they do in the process of performance? In this paper I will focus on the harpsichord playing, and would like to make clear that "good" playing would be "fantasying" with "discretion". For that purpose I will examine the works with "written out improvisations" by German keyboard player J. J. Froberger (1616-1667) and his contemporary keyboard schools, and analyze how players handle the keyboard in the process of playing. By doing this we can become aware of attempts to make the sound of the instrument more sonorous and find out various ways of devising through "economical" use of fingers by players themselves. But what we must take special notice of here is not only the technical treatments related to fingers and the instrument, but also players' appropriate judgement, which we can call "discretion". And if players, comprehending the style of the works and tailoring each performance suited to each occasion (when and where), have the collective strength of playing with this discretion, that is exactly "fantasying". The term "Fantasy" has been used to indicate player's flashes of genius, but in reality active "fantasying" is "good" playing.