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...not decline monotonically but I would expect it to have a decreasing trend!) I may just be confused, but I *think* the issue is somewhere within the log-likelihood calculation for gls. The example below compares a series of spline fits to a simulated exponentially decreasing data set with some heteroscedasticity; a more detailed example comparing fits of lm() and gls() to a simpler simulation [linear regression] shows similar, although less extreme, behavior, and is posted at http://www.zoo.ufl.edu/bolker/splinelik.Rnw (or http://www.zoo.ufl.edu/bolker/splinelik.pdf ). Apologies for boneheade...