  The Heisenberg limit to laser coherence $\mathfrak{C}$ -- the number of
photons in the maximally populated mode of the laser beam -- is the fourth
power of the number of excitations inside the laser. We generalize the previous
proof of this upper bound scaling by dropping the requirement that the beam
photon statistics be Poissonian (i.e., Mandel's $Q=0$). We then show that the
relation between $\mathfrak{C}$ and sub-Poissonianity ($Q<0$) is win-win, not a
tradeoff. For both regular (non-Markovian) pumping with semi-unitary gain
(which allows $Q\xrightarrow{}-1$), and random (Markovian) pumping with
optimized gain, $\mathfrak{C}$ is maximized when $Q$ is minimized.
