is to say a family $(Y^n,Z^n)$ of solutions to BSDEs satisfying$$\label{eq:BSDEn}
Y^n_t =\xi +\int_t^T f(s,Y_s^{n-1},Z_s^{n-1}) ds -\int_t^T Z_s^n dW_s, \quad t\in [0,T],$$ where $Y^0\equiv Z^0\equiv 0$. Then, a fixed point argument allows one to construct, in appropriate spaces, a solution $(Y,Z)$ to Equation . If $\xi$ and $f(t,y,z)$ are Malliavin differentiable, then so is $(Y^n,Z^n)$. Then, it just remains to prove that this property extends to the limits $Y$ and $Z$ of respectively $Y^n$ and $Z^n$, in appropriate spaces. More precisely this is done by a uniform (in $n$) control of the Sobolev norms of $Y^n,Z^n$ or equivalently by proving that the Malliavin derivatives $(DY^n,DZ^n)$ of $(Y^n,Z^n$) converge to the solution of a linear BSDE whose solution will be the Malliavin derivatives $(DY, DZ)$ of $Y$ and $Z$. This last step is exactly where the extra regularity (EPQ1)-(EPQ2) is needed. It appears quite clearly that for this approach, the conditions of [@EPQ] cannot be optimized in the general case. Even though this idea seems pretty natural, it is based on a choice somehow arbitrary. Indeed, a necessary condition for $DY_t$ to be well-defined at a given time $t$, is that there exists a sequence of random variables $(F^n)_n$ converging to 