We investigate integer partitions $\lambda$ of $n$ that are nearly self-conjugate in the sense there $n - 1$ overlapping cells among Ferrers diagram and its transpose, by establishing a correspondence, through method combinatorial telescoping, to which (i).~there exists at least one even part; (ii).~any part is size $2$; (iii).~the odd parts distinct; (iv).~no $1$. In particular, this correspon...