  We present the analysis of two recently proposed noise reduction techniques,
Hutch++ and XTrace, both based on inexact deflation. These methods were proven
to have a better asymptotic convergence to the solution than the classical
Girard-Hutchinson stochastic method. We applied these methods to the
computation of the trace of the inverse of the Dirac operator with $O(a)$
improved Wilson fermions on the QCD ensemble generated by the RC$^{\star}$
collaboration with $m_{\pi}\approx 400$ MeV and $V = 64\times 32^3$.
Unfortunately, we see no noise reduction with a moderate number of sources, and
we attempt an explanation of why this is the case. This study was part of the
effort to evaluate isospin-breaking effects using the RM123 with C$^{\star}$
boundary conditions in an unquenched set-up.
