  Gauge fixing may be done in different ways. We show that using the chain
structure to describe a constrained system, enables us to use either a perfect
gauge, in which all gauged degrees of freedom are determined; or an imperfect
gauge, in which some first class constraints remain as subsidiary conditions to
be imposed on the solutions of the equations of motion. We also show that the
number of constants of motion depends on the level in a constraint chain in
which the gauge fixing condition is imposed. The relativistic point particle,
electromagnetism and the Polyakov string are discussed as examples and perfect
or imperfect gauges are distinguished.
