  A simple scheme was proposed by Knuth to generate binary balanced codewords
from any information word. However, this method is limited in the sense that
its redundancy is twice that of the full sets of balanced codes. The gap
between Knuth's algorithm's redundancy and that of the full sets of balanced
codes is significantly considerable. This paper attempts to reduce that gap.
Furthermore, many constructions assume that a full balancing can be performed
without showing the steps. A full balancing refers to the overall balancing of
the encoded information together with the prefix. We propose an efficient way
to perform a full balancing scheme that does not make use of lookup tables or
enumerative coding.
