  We point out a general problem with the procedures commonly used to obtain
improved actions from MCRG decimated configurations. Straightforward
measurement of the couplings from the decimated configurations, by one of the
known methods, can result into actions that do not correctly reproduce the
physics on the undecimated lattice. This is because the decimated
configurations are generally not representative of the equilibrium
configurations of the assumed form of the effective action at the measured
couplings. Curing this involves fine-tuning of the chosen MCRG decimation
procedure, which is also dependent on the form assumed for the effective
action. We illustrate this in decimation studies of the SU(2) LGT using
Swendsen and Double Smeared Blocking decimation procedures. A single-plaquette
improved action involving five group representations and free of this pathology
is given.
