  We determine quark mass dependent order $a$ improvement terms of the form
$b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents,
using correlators in coordinate space. We use a set of CLS ensembles comprising
non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz
gauge action at $\beta=3.4,3.46,3.55$ and $\beta=3.7$, corresponding to lattice
spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the
$b_J$ improvement coefficients which are proportional to non-singlet quark mass
combinations and also discuss the possibility of determining the $\bar{b}_J$
coefficients which are proportional to the trace of the quark mass matrix.
