  It is known that many (upper) cluster algebras possess different kinds of
good bases which contain the cluster monomials and are parametrized by the
tropical points of cluster Poisson varieties. For a large class of upper
cluster algebras (injective-reachable ones with full rank coefficients), we
describe all of its bases with these properties. Moreover, we show the
existence of the generic basis for them. In addition, we prove that
Bridgeland's representation theoretic formula is effective for their theta
functions (weak genteelness).
  Our results apply to (almost) all well-known cluster algebras arising from
representation theory or higher Teichm\"uller theory, including quantum affine
algebras, unipotent cells, double Bruhat cells, skein algebras over surfaces,
where we change the coefficients if necessary so that the full rank assumption
holds.
