  We study and propose schemes that map messages onto constant-weight codewords
using variable-length prefixes. We provide polynomial-time computable formulas
that estimate the average number of redundant bits incurred by our schemes. In
addition to the exact formulas, we also perform an asymptotic analysis and
demonstrate that our scheme uses $\frac12 \log n+O(1)$ redundant bits to encode
messages into length-$n$ words with weight $(n/2)+{\sf q}$ for constant ${\sf
q}$. We also propose schemes that map messages into balanced codebooks with
error-correcting capabilities. For such schemes, we provide methods to
enumerate the average number of redundant bits.
