A morphic ring of neat range one

We show that a commutative ring $R$ has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring $R$ has a neat range one if and only if for any elements $a, b \in R$ such that $aR=bR$ there exist neat elements $s, t \in R$ such that $bs=c$, $ct=b$. Examples of morphic rings of neat range one are given.