  We test a recent proposal to use approximate trivializing maps in a field
theory to speed up Hybrid Monte Carlo simulations. Simulating the CP^{N-1}
model, we find a small improvement with the leading order transformation, which
is however compensated by the additional computational overhead. The scaling of
the algorithm towards the continuum is not changed. In particular, the effect
of the topological modes on the autocorrelation times is studied.
