Abstract. Let k be a field and A a finite-dimensional algebra. An A-module M will be called a bristle module, provided it is generated by indecomposable submodules of length 2. An indecomposable bristle module has Loewy length at most 2 and its socle is homogeneous. We are going to study bristle modules where also the top is homogeneous. In case k is algebraically closed, we may assume that A is a (generalized) Kronecker algebra. As we will see, for a Kronecker algebra, there is an abundance of bristle modules. The first invariant of a bristle module is its bristle variety, this is a projective variety and any projective variety occurs in this way. In this way, the study of submodules of length 2 has to be considered as a basic encounter between representation theory and algebraic geometry.