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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⩽ N, the overlaps between these trial wavefunctions and the corresponding exact solutions 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⩽ 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 wavefunctions at L⩽ N and that of their CF counterparts. Results are given for two different projection methods commonly …