diff --git a/draft.tex b/draft.tex
index 9769bb5..e4ca6b3 100644
--- a/draft.tex
+++ b/draft.tex
@@ -283,7 +283,8 @@
 and Lattice results~\cite{Becirevic:2006nm,Horgan:2013hoa}, 
 %sure full agreement among the LCSRs and Lattice results.
 uncertainties on the form factors parameters are doubled with respect to Ref.~\cite{Straub:2015ica}},
-the $\mathcal{H}_\lambda(q^{2})$ 
+the $\mathcal{H}_\lambda(q^{2})$ encode the aforementioned non-factorisable
+hadronic contribution and
 are described using two complementary parametrisations~\cite{Bobeth:2017vxj,Hurth:2017sqw} - 
 for brevity only a subset of results is shown for the latter approach.
 In the following this function is expressed in terms of a ``conformal'' 
@@ -315,8 +316,10 @@
 Therefore, in a common framework these hadronic contributions are treated as 
 nuisance parameters, while only the Wilson coefficients $\widetilde{\WC}_9^{(\mu,e)}$ 
 and $\widetilde{\WC}_{10}^{(\mu,e)}$ are kept separately for the two channels.
-For consistency the WC $\widetilde{C}_{7}$ is also shared in the fit, 
-given its universal coupling to photons~\cite{Paul:2016urs}. 
+For consistency the WC $\widetilde{C}_{7}$ is also shared in the fit 
+and fixed to its SM value, given its universal coupling to photons
+and the strong constraint from radiative $B$ decays~\cite{Paul:2016urs}. 
+Similarly, all the right-handed WCs are fixed to their SM values, \textit{i.e.} $\WC_i^{\prime\,(\mu,e)} = 0$.
 
 Signal-only ensembles of pseudo-experiments are generated with
 sample size corresponding roughly to the yields foreseen in LHCb Run-II [$8\,$fb$^{-1}$] and future upgrades 
@@ -357,8 +360,8 @@
 %
 \begin{enumerate}
     %
-    \item[i.] baseline $\mathcal{H}_\lambda[z^2]$ SM prediction 
-    parametrisation~\cite{Bobeth:2017vxj} as a multivariate Gaussian constraint;
+    \item[i.] baseline $\mathcal{H}_\lambda[z^2]$ SM prediction~\cite{Bobeth:2017vxj} 
+    included as a multivariate Gaussian constraint;
     %
     \item[ii.] no theoretical assumption on $\mathcal{H}_\lambda[z^2]$ 
     and with free-floating parameters;
@@ -368,14 +371,14 @@
     %
     \item[iv.] and re-parametrisation of its description as  
       proposed in Ref.~\cite{Hurth:2017sqw}, \textit{i.e.}
-      using instead a series of $1 + a_{\lambda} + b_{\lambda}(q^{2}/6\,$GeV$^{2})$. 
+      using instead an expansion in terms of $1 + a_{\lambda} + b_{\lambda}(q^{2}/6\,$GeV$^{2})$. 
 
     %
 \end{enumerate}
 %
-The stability of the model and the convergency to the global minimum is enforced by
-repeating the fit with randomised starting parameters; 
-the solution with smallest negative log-likelihood is taken as the default. 
+%The stability of the model and the convergency to the global minimum is enforced by
+%repeating the fit with randomised starting parameters; 
+%the solution with smallest negative log-likelihood is taken as the default. 
 
  
 Figure~\ref{fig:C9ellipse} shows the fit results for several alternative parametrisations 
@@ -488,12 +491,13 @@
 including a set of values that minimises the tension with the $P_5'$ 
 anomaly~\cite{Aaij:2015oid}, while keeping $\WC_9^{(\mu)}$ and
 $\WC_{10}^{(\mu)}$ at their SM values.
-Despite the mis-modelling of the non-local hadronic effects in the fit results, we observe 
+Despite the mis-modelling of the non-local hadronic effects in the fit, we observe 
 that the determination of $\Delta\WC_9$ and $\Delta\WC_{10}$ is always unbiased, 
 thanks to the relative cancellation of all the shared parameters between the two channels.
-It is worth emphasizing that a hypothetical determination of the individual  
-$\widetilde{\WC}_9^{(\mu,e)}$ and $\widetilde{\WC}_{10}^{(\mu,e)}$ WCs would result
-in a strong bias that mimics the behaviour of NP and makes impossible any claim in this direction.
+It is worth mentioning that a hypothetical determination of the individual  
+$\widetilde{\WC}_9^{(\mu,e)}$ and $\widetilde{\WC}_{10}^{(\mu,e)}$ WCs 
+can also produce a shift in their central values
+that mimics the behaviour of NP~\cite{Mauri:2018}.% and makes impossible any claim in this direction.
 
 
 %