  I present a new approach at deriving far-infrared photometric redshifts for
galaxies based on their reprocessed emission from dust at rest-frame
far-infrared through millimeter wavelengths. Far-infrared photometric redshifts
("FIR-$z$") have been used over the past decade to derive redshift constraints
for highly obscured galaxies that lack photometry at other wavelengths like the
optical/near-infrared. Most literature FIR-z fits are performed through
$\chi^2$minimization to a single galaxy's far-infrared template spectral energy
distribution (SED). The use of a single galaxy template, or modest set of
templates, can lead to an artificially low uncertainty estimate on FIR-$z$'s
because real galaxies display a wide range in intrinsic dust SEDs. I use the
observed distribution of galaxy SEDs (for well-constrained samples across
$0<z<5$) to motivate a new far-infrared through millimeter photometric redshift
technique called MMpz. The MMpz algorithm asserts that galaxies are most likely
drawn from the empirically observed relationship between rest-frame peak
wavelength, $\lambda_{\rm peak}$, and total IR luminosity, L$_{\rm IR}$; the
derived photometric redshift accounts for the measurement uncertainties and
intrinsic variation in SEDs at the inferred L$_{\rm IR}$, as well as heating
from the CMB at $z>5$. The MMpz algorithm has a precision of $\sigma_{\Delta
z/(1+z)}\approx0.3-0.4$, similar to single-template fits, while providing a
more accurate estimate of the FIR-$z$ uncertainty with reduced chi-squared of
order $\mathcal{O}(\chi^2_{\nu})=1$, compared to alternative far-infrared
photometric redshift techniques (with
$\mathcal{O}(\chi^2_{\nu})\approx10-10^{3}$).
