We analyse and generalize recently proposed noise reduction methods for  
nonlinear chaotic time sequences with additive noise. All these methods  
have in common that they work iteratively, and that in each step of the  
iteration the noise is suppressed by requiring locally linear relations  
among the delay coordinates, i.e. by moving the delay vectors towards  
some smooth manifold. The different methods can be compared unambiguously  
in the case of strictly hyperbolic systems corrupted by measurement noise  
of infinitesimally low level. We find that all proposed methods converge  
in this ideal case, but not equally fast. Different problems arise if the  
system is not hyperbolic, and at higher noise levels. We propose and  
test a new scheme which seems to avoid most of  
these problems, and seems to give the best noise reduction so far.  
Moreover, large improvements are possible within the new scheme and the  
previous schemes if their parameters are not kept fixed during  
the iteration, and if corrections are included which take into account  
the curvature of the attracting manifold. Finally, we stress that  
comparison with simple low-pass filters tends to overestimate the  
relative achievements of these non-linear noise reduction schemes, and  
suggest that they should be compared to Wiener-type filters.