  We deal with two forms of the "uniqueness cases" in the classification of
large simple $K^*$-groups of finite Morley rank of odd type, where large means
the $m_2(G)$ at least three. This substantially extends results known for even
larger groups having \Prufer 2-rank at least three, to cover the two groups
$\PSp_4$ and $\G_2$. With an eye towards distant developments, we carry out
this analysis for $L^*$-groups which is substantially broader than the $K^*$
setting.
