  Construction sequences are a general method of building symbolic shifts that
capture cut-and-stack constructions and are general enough to give symbolic
representations of Anosov-Katok diffeomorphisms. We show here that any finite
entropy system that has an odometer factor can be represented as a special
class of construction sequences, the odometer based construction sequences
which correspond to those cut-and-stack constructions that do not use spacers.
We also show that any additional property called the "small word condition" can
also be satisfied in a uniform way.
