  We study scalar one-loop amplitudes in massive $\phi^3$-theory within causal
loop-tree duality. We derive a recurrence relation for the integrand of the
amplitude. The integrand is by construction free of spurious singularities on
H-surfaces. Taking renormalisation and contour deformation into account, we
obtain the (integrated) amplitude by Monte Carlo integration. We have checked
up to seven points that our results agree with analytic results.
