  We use filtered modules over a Noetherian ring and fibred bounded control on
homomorphisms to construct a new kind of controlled algebra with applications
in geometric topology. The theory here can be thought of as a "pushout" of the
bounded K-theory with fibred control and the controlled G-theory constructed
and used by the authors. This paper contains the non-equivariant theory
including controlled excision theorems crucial for computations.
