  A ring $R$ is a UU ring if every unit is unipotent, or equivalently if every
unit is a sum of a nilpotent and an idempotent that commute. These rings have
been investigated in C\u{a}lug\u{a}reanu \cite{C} and in Danchev and Lam
\cite{DL}. In this paper, two generalizations of UU rings are discussed. We
study rings for which every unit is a sum of a nilpotent and an idempotent, and
rings for which every unit is a sum of a nilpotent and two idempotents that
commute with one another.
