  In this paper we study the question of whether on smooth projective surfaces
the denominators in the volumes of big line bundles are bounded. In particular
we investigate how this condition is related to bounded negativity (i.e., the
boundedness of self-intersections of irreducible curves). Our first result
shows that boundedness of volume denominators is equivalent to \emph{primitive
bounded negativity}, which in turn is implied by bounded negativity. We connect
this result to the study of semi-effective orders of divisors: Our second
result shows that negative classes exist that become effective only after
taking an arbitrarily large multiple.
