  In a triangulated category, cofibre fill-ins always exist. Neeman showed that
there is always at least one "good" fill-in, i.e., one whose mapping cone is
exact. Verdier constructed a fill-in of a particular form in his proof of the
$4 \times 4$ lemma, which we call "Verdier good". We show that for several
classes of morphisms of exact triangles, the notions of good and Verdier good
agree. We prove a lifting criterion for commutative squares in terms of
(Verdier) good fill-ins. Using our results on good fill-ins, we also prove a
pasting lemma for homotopy cartesian squares.
