  We describe a tunable-cavity QED architecture with an rf SQUID phase qubit
inductively coupled to a single-mode, resonant cavity with a tunable frequency
that allows for both microwave readout of tunneling and dispersive measurements
of the qubit. Dispersive measurement is well characterized by a three-level
model, strongly dependent on qubit anharmonicity, qubit-cavity coupling and
detuning. A tunable cavity frequency provides a way to strongly vary both the
qubit-cavity detuning and coupling strength, which can reduce Purcell losses,
cavity-induced dephasing of the qubit, and residual bus coupling for a system
with multiple qubits. With our qubit-cavity system, we show that dynamic
control over the cavity frequency enables one to avoid Purcell losses during
coherent qubit evolutions and optimize state readout during qubit measurements.
The maximum qubit decay time $T_1$ = 1.5 $\mu$s is found to be limited by
surface dielectric losses from a design geometry similar to planar transmon
qubits.
