  Mapping complex problems to simpler effective models is a key tool in
theoretical physics. One important example in the realm of strongly correlated
fermionic systems is the mapping of the Hubbard model to a t-J model which is
appropriate for the treatment of doped Mott insulators. Charge fluctuations
across the charge gap are eliminated. So far the derivation of the t-J model is
only known at half-filling or in its immediate vicinity. Here we present the
necessary conceptual advancement to treat finite doping. The results for the
ensuing coupling constants are presented. Technically, the extended derivation
relies on self-similar continuous unitary transformations (sCUT) and
normal-ordering relative to a doped reference ensemble. The range of
applicability of the derivation of t-J model is determined as function of the
doping $\delta$ and the ratio bandwidth W over interaction U.
