  In this paper we present the first systematic analysis of the impact of the
populated vs. intrinsic spin distribution on the nuclear level density and
$\gamma$-ray strength function retrieved through the Oslo Method. We illustrate
the effect of the spin distribution on the recently performed
$^{239}\mathrm{Pu}$(d,p$\gamma$)$^{240}\mathrm{Pu}$ experiment using a 12 MeV
deuteron beam performed at the Oslo Cyclotron Lab. In the analysis we couple
state-of-the-art calculations for the populated spin-distributions with the
Monte-Carlo nuclear decay code RAINIER to compare Oslo Method results to the
known input. We find that good knowledge of the populated spin distribution is
crucial and show that the populated distribution has a significant impact on
the extracted nuclear level density and $\gamma$-ray strength function for the
$^{239}\mathrm{Pu}$(d,p$\gamma$)$^{240}\mathrm{Pu}$ case.
