We describe a realistic, renormalizable, supersymmetric ''quindecuplet'' model in which the top quark, left-handed bottom quark, and up-type Higgs boson are composite, with a compositeness scale similar to 1-3 TeV. The top-quark-Higgs-boson Yukawa coupling is a dynamically generated strong interaction effect, and is naturally much larger than any other Yukawa coupling. The light-quark doublets and right-handed up-type quarks are also composite but at higher energies; the hierarchy of quark masses and mixings is due to a hierarchy in the compositeness scales. Flavor-changing neutral currents are naturally suppressed, as is baryon-number violation by Planck-scale dimension-five operators. The model predicts that the most easily observable effects would be on b-quark physics and on the rho parameter. In particular, a small negative Delta rho= -epsilon leads to Delta R-b> + 2 epsilon. There are effects on B-meson mixing and on flavor-changing neutral-current b-quark decays to leptons which might be detectable, but not on b-->s gamma. The model also suggests the supersymmetry-breaking mass for the right-handed top squark might be considerably larger than that of the left-handed top squark.