  We study when the stable category of an abelian category modulo a full
additive subcategory is balanced and, in case the subcategory is functorially
finite, we study a weak version of balance. Precise necessary and sufficient
conditions are given in case the subcategory is either a Serre class or a class
consisting of projective objects. The results in this second case apply very
neatly to (generalizations of) hereditary abelian categories.
