  The sign problem in quantum Monte Carlo calculations is analyzed using the
meron-cluster solution. The concept of merons can be used to solve the sign
problem for a limited class of models. Here we show that the method can be used
to \textit{reduce} the sign problem in a wider class of models. We investigate
how the meron solution evolves between a point in parameter space where it
eliminates the sign problem and a point where it does not affect the sign
problem at all. In this intermediate regime the merons can be used to reduce
the sign problem. The average sign still decreases exponentially with system
size and inverse temperature but with a different prefactor. The sign exhibits
the slowest decrease in the vicinity of points where the meron-cluster solution
eliminates the sign problem. We have used stochastic series expansion quantum
Monte Carlo combined with the concept of directed loops.
