  Currently, the primordial helium abundance is best estimated through
spectroscopic observations of H II regions in metal-poor galaxies. However
these determinations are limited by several systematic uncertainties which
ultimately limit our ability to accurately ascertain the primordial abundance.
In this study, we improve the methodologies for solving for the reddening, the
emission contributions from collisional excitation of the H I atoms, the
effects underlying absorption in the H I and He I emission lines, and the
treatment of the blended H I and He I emission at $\lambda$3889 with the aim of
lowering the systematic uncertainties in helium abundance determinations. To
apply these methods, we have obtained observations of the He I $\lambda$10830
emission line in the brightest H II region in the extremely metal-poor (3$\%$
Z$_{\odot}$) galaxy Leo P with the LUCI1 instrument on the LBT. We combine this
measurement with previous MODS/LBT observations to derive an improved helium
abundance. In doing so, our present analysis results in a decrease in the
uncertainty in the helium abundance of Leo P by approximately 70%. This result
is combined with data from other observations to estimate the primordial helium
mass fraction, Y$_{p}$ $=$ 0.2453 $\pm$ 0.0034.
