  A tournament $T$ is a tournament completion of a bipartite tournament $D$ if
$D$ is a spanning subdigraph of $T$, i.e., $V(D)=V(T)$ and $A(D)\subseteq
A(T)$. If $C$ is a $k$-dicycle (i.e., directed cycle of length $k$) in a
tournament completion $T$ of $D$ and $C$ is not a dicycle in $D$, i.e.,
$A(C)\subseteq A(T)$ and $A(C)\not\subseteq A(D)$, then we call $C$ an
augmented $k$-dicycle of $T$. In this paper, we investigate the families of
bipartite tournaments for which there exists a tournament completion with
exactly one augmented $3$-dicycle and with no augmented $4$-dicycles. Our
investigation may be viewed as a variant of the orientation completion problem
initiated by Bang-Jensen et al..
