  We revisit the composite fermion (CF) construction of the lowest angular
momentum yrast states of rotating Bose gases with weak short range interaction.
For angular momenta at and below the single vortex, $L \leq N$, the overlaps
between these trial wave functions and the corresponding exact solutions {\it
increase} with increasing system size and appear to approach unity in the
thermodynamic limit. In the special case $L=N$, this remarkable behaviour was
previously observed numerically. Here we present methods to address this point
analytically, and find strongly suggestive evidence in favour of similar
behaviour for all $L \leq N$. While not constituting a fully conclusive proof
of the converging overlaps, our results do demonstrate a striking similarity
between the analytic structure of the exact ground state wave functions at $L
\leq N$, and that of their CF counterparts. Results are given for two different
projection methods commonly used in the CF approach.
