  We study theoretically a quantum dot in the quantum Hall regime that is
strongly coupled to a single lead via a point contact. We find that even when
the transmission through the point contact is perfect, important features of
the Coulomb blockade persist. In particular, the tunneling into the dot via a
second weakly coupled lead is suppressed, and shows features which can be
ascribed to elastic or inelastic cotunneling through the dot. When there is
weak backscattering at the point contact, both the tunneling conductance and
the differential capacitance are predicted to oscillate as a function of gate
voltage. We point out that the dimensionless ratio $\xi$ between the fractional
oscillations in $G$ and $C$ is an intrinsic property of the dot, which, in
principle, can be measured. We compute $\xi$ within two models of
electron-electron interactions. In addition, we discuss the role of additional
channels.
