  We study the range of a classifiable class ${\cal A}$ of unital separable
simple amenable $C^*$-algebras which satisfy the Universal Coefficient Theorem.
The class ${\cal A}$ contains all unital simple AH-algebras. We show that all
unital simple inductive limits of dimension drop circle $C^*$-algebras are also
in the class. This unifies some of the previous known classification results
for unital simple amenable $C^*$-algebras. We also show that there are many
other $C^*$-algebras in the class. We prove that, for any partially ordered,
simple weakly unperforated rationally Riesz group $G_0$ with order unit $u,$
any countable abelian group $G_1,$ any metrizable Choquet simplex $S,$ and any
surjective affine continuous map $r: S\to S_u(G_0)$ (where $S_u(G_0)$ is the
state space of $G_0$) which preserves extremal points, there exists one and
only one (up to isomorphism) unital separable simple amenable $C^*$-algebra $A$
in the classifiable class ${\cal A}$ such that $$ ((K_0(A), K_0(A)_+, [1_A]),
K_1(A), T(A), \lambda_A)=((G_0, (G_0)_+, u), G_1,S, r).
