  We show that in a category with pullbacks, arbitrary sifted colimits may be
constructed as filtered colimits of reflexive coequalizers. This implies that
"lex sifted colimits", in the sense of Garner--Lack, decompose as
Barr-exactness plus filtered colimits commuting with finite limits. We also
prove generalizations of these results for $\kappa$-small sifted and filtered
colimits, and their interaction with $\lambda$-small limits in place of finite
ones, generalizing Garner's characterization of algebraic exactness in the
sense of Ad\'amek--Lawvere--Rosick\'y. Along the way, we prove a general result
on classes of colimits, showing that the $\kappa$-small restriction of a
saturated class of colimits is still "closed under iteration".
