We develop a birth-death model for a cavity QED laser and analyze the dependence of the lasing threshold on the fraction, β, of spontaneous emission directed into the laser mode. We define threshold in terms of the Fano factor for the intracavity phonon number. We emphasize the role of β as a parameter characterizing the ‘‘system size’’and show that the concept of laser threshold is well-defined in the ‘‘thermodynamic’’limit, β− 1→∞. An ideal cavity-QED laser operates far outside this limit and therefore, in contrast to a conventional laser, is not a threshold device. We present numerical results showing how this difference affects the noise properties of the device.