Building on the general equilibrium analysis conducted by the authors in "Output-Based Allocations of Emissions Permits: Efficiency and Distributional Effects in a General Equilibrium Setting with Taxes and Trade," this paper sets out to expand on one of the central findings of the first paper. For a cap-and-trade scheme, in the absence of other market failures, lump-sum distributions of emissions permits, like auctions or grandfathering, are equally efficient. Meanwhile, output-based allocation (OBA) is an inefficient mechanism, due to the implicit output subsidy granted, which discourages conservation as a means of emissions reduction. However, in a second-best world with tax and trade distortions, OBA does have features that make it appealing from an economic efficiency standpoint. First, it mitigates the price rises that tend to exacerbate pre-existing tax distortions to the labor market. Second, OBA potentially results in much lower rates of carbon leakage from the implementing country to the rest of world. It may also prevent leakage toward unregulated sectors within the subject economy. Finally, from a political standpoint, it may help minimize the political difficulties of achieving emissions reductions goals, given competitiveness concerns. Still, tradeoffs exist between achieving these different goals. This paper will analyze these potential tradeoffs of choosing different allocation mechanisms in order to achieve overall emissions reductions goals while minimizing intra- and international leakage and minimizing the traditional measures of welfare loss associated with emissions reductions. The goal of the paper is to propose certain rules for identifying sectors and mechanisms for minimizing the costs of broader emissions reduction when considering the interaction of one country's emissions policies with unregulated emissions and labor market distortions. The analysis is carried out in a modified GTAP framework augmented with a labor-leisure choice for workers and documented in the previous paper. Such a framework allows for the consideration of how distortionary tax instruments may be offset by revenues generated from permit auctions or may be exacerbated by policies that raise prices. The current implementation relies on the GTAP version 5 database, although efforts are underway to update to the GTAP version 6 database. While this update is useful from a policy perspective, it is not necessary to the central purpose of this paper, that is, to analyze the relative effectiveness of different emissions policies in a world with pre-existing tax distortions.