The paper investigates the locus of non-simple principally polarised abelian g-folds. We show that the irreducible components of this locus are IsgD, defined as the locus of principally polarised g-folds having an abelian subvariety with restricted polarisation of type D=(d1,…,dk), where k≤g2. The main theorem produces Humbert-like equations for irreducible components of IsgD for any g and D. Moreover, there are theorems which characterise the Jacobians of curves that are étale double covers or double covers branched in two or four points.