  Nonlinear networks can host spatially compact time periodic solutions called
compact breathers. Such solutions can exist accidentally (i.e. for specific
nonlinear strength values) or parametrically (i.e. for any nonlinear strength).
In this work we introduce an efficient generator scheme for one-dimensional
nonlinear lattices which support either types of compact breathers spanned over
a given number U of lattice's unit cells and any number of sites v per cell -
scheme which can be straightforwardly extended to higher dimensions. This
scheme in particular allows to show the existence and explicitly construct
examples of parametric compact breathers with inhomogeneous spatial profiles --
extending previous results which indicated that only homogeneous parametric
compact breathers exist. We provide explicit d=1 lattices with different v
supporting compact breather solutions for U=1,2.
