  We investigate the confining phase vacua of supersymmetric $Sp(2\NC)$ gauge
theories that contain matter in both fundamental and antisymmetric
representations. The moduli spaces of such models with $\NF=3$ quark flavors
and $\NA=1$ antisymmetric field are analogous to that of SUSY QCD with
$\NF=\NC+1$ flavors. In particular, the forms of their quantum superpotentials
are fixed by classical constraints. When mass terms are coupled to
$W_{(\NF=3,\NA=1)}$ and heavy fields are integrated out, complete towers of
dynamically generated superpotentials for low energy theories with fewer
numbers of matter fields can be derived. Following this approach, we deduce
exact superpotentials in $Sp(4)$ and $Sp(6)$ theories which cannot be
determined by symmetry considerations or integrating in techniques. Building
upon these simple symplectic group results, we also examine the ground state
structures of several $Sp(4) \times Sp(4)$ and $Sp(6) \times Sp(2)$ models. We
emphasize that the top-down approach may be used to methodically find dynamical
superpotentials in many other confining supersymmetric gauge theories.
