Formality quasi-isomorphisms Cobar(C) {> O are often constructed via transcendental methods, resulting in quasi-isomorphisms de ned over extensions of Q. By showing that they can be constructed recursively simply by solving systems of linear equations over Q, in this talk we will show that these formality quasi-isomorphisms can be "demystifi ed" for a large class of dg-operads, given certain assumptions on H(O). This result is motivated by applications to deformation quantization, and to computationof the rational homotopy groups of embedding spaces. This talk is based on a paper in preparation joint with V.A. Dolgushev.