  The problem of the two-level atom laser is studied analytically. The
steady-state solution is expressed as a continued fraction, and allows for
accurate approximation by rational functions. Moreover, we show that the abrupt
change observed in the pump dependence of the steady-state population is
directly connected with the transition to the lasing regime. The condition for
a sharp transition to Poissonian statistics is expressed as a scaling limit of
vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$,
such that $g^2/\kappa$ stays finite and $g^2/\kappa > 2 \gamma$, where $\gamma$
is the rate of atomic losses. The same scaling procedure is also shown to
describe a similar change to Poisson distribution in the Scully-Lamb laser
model too, suggesting that the low-$\kappa$, low-$g$ asymptotics is of a more
general significance for the laser transition.
