  Techniques to retrieve the atmospheric properties of exoplanets via direct
observation of their reflected light have often been limited in scope due to
computational constraints imposed by the forward-model calculations. We have
developed a new set of techniques which significantly decreases the time
required to perform a retrieval while maintaining accurate results. We
constructed a grid of 1.4 million pre-computed geometric albedo spectra valued
at discrete sets of parameter points. Spectra from this grid are used to
produce models for a fast and efficient nested sampling routine called PSGnest.
Beyond the upfront time to construct a spectral grid, the amount of time to
complete a full retrieval using PSGnest is on the order of seconds to minutes
using a personal computer. An extensive evaluation of the error induced from
interpolating intermediate spectra from the grid indicates that this bias is
insignificant compared to other retrieval error sources, with an average
coefficient of determination between interpolated and true spectra of 0.998. We
apply these new retrieval techniques to help constrain the optimal bandpass
centers for retrieving various atmospheric and bulk parameters from a
LuvEx-type mission observing several planetary archetypes. We show that
spectral observations made using a 20\% bandpass centered at 0.73 microns can
be used alongside our new techniques to make detections of $H_2O$ and $O_2$
without the need to increase observing time beyond what is necessary for a
signal-to-noise ratio of 10. The methods introduced here will enable robust
studies of the capabilities of future observatories to characterize exoplanets.
