  The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$
samples behaves like $1/\sqrt{N}$. This scaling makes it often very time
intensive to reduce the error of computed observables, in particular for
applications in lattice QCD. It is therefore highly desirable to have
alternative methods at hand which show an improved error scaling. One candidate
for such an alternative integration technique is the method of recursive
numerical integration (RNI). The basic idea of this method is to use an
efficient low-dimensional quadrature rule (usually of Gaussian type) and apply
it iteratively to integrate over high-dimensional observables and Boltzmann
weights. We present the application of such an algorithm to the topological
rotor and the anharmonic oscillator and compare the error scaling to MCMC
results. In particular, we demonstrate that the RNI technique shows an error
scaling in the number of integration points $m$ that is at least exponential.
