  We study the phase structure of N = 1 supersymmetric Sp(2N_c) gauge theories
with 2N_f fundamentals, an adjoint, and vanishing superpotential. Using
a-maximization, we derive analytic expressions for the values of N_f below
which the first several gauge-invariant operators in the chiral ring violate
the unitarity bound and become free fields. In doing so we are able to
explicitly check previous conjectures about the behavior of this theory made by
Luty, Schmaltz, and Terning. We then compare this to an analysis of the first
two 'deconfined' dual descriptions based on the gauge groups Sp(2N_f+2) x
SO(2N_c+5) and Sp(2N_f+2) x SO(4N_f+4) x Sp(2N_c+2), finding precise agreement.
In particular, we find no evidence for non-obvious accidental symmetries or the
appearance of a mixed phase in which one of the dual gauge groups becomes free.
