  Measurements of 21 cm Epoch of Reionization (EoR) structure are subject to
systematics originating from both the analysis and the observation conditions.
Using 2013 data from the Murchison Widefield Array (MWA), we show the
importance of mitigating both sources of contamination. A direct comparison
between results from Beardsley et al. 2016 and our updated analysis
demonstrates new precision techniques, lowering analysis systematics by a
factor of 2.8 in power. We then further lower systematics by excising
observations contaminated by ultra-faint RFI, reducing by an additional factor
of 3.8 in power for the zenith pointing. With this enhanced analysis precision
and newly developed RFI mitigation, we calculate a noise-dominated upper limit
on the EoR structure of $\Delta^2 \leq 3.9 \times 10^3$ mK$^2$ at $k=0.20$
$\textit{h}$ Mpc$^{-1}$ and $z=7$ using 21 hr of data, improving previous MWA
limits by almost an order of magnitude.
