These new information lead me to this old topic on the forum :
It seems that my situation is similar.
The function I try to minimize is the negative log likelihood of a 10 bin Poisson counting :
\begin{equation}
L(\mu, rescale) = \prod_i=1^10 Poisson(n_i | \mu_i * s_i(rescale) + b_i(rescale) )
\end{equation}
Re-scaling the NLL by a factor beta may help the numerical minimization.
Then I guess that I should compensate the computed error by a factor sqrt(beta) ?
Similarly to what is written in section 1.4.1 of the documentation.
Or is it better to re-scale the UP parameter ? (which I believe is the same as ErrorDef)