The paper uses a computable general equilibrium (CGE) model of Tanzania, that includes considerable factor disaggregation and household detail, to explore the impact of trade liberalization on growth and poverty alleviation. The focus is on the impact of trade liberalization policies under different structural constraints, such as large marketing margins between producers and the market. The first major conclusion that obtains from the empirical results is that the nature of the macroeconomic and sectoral market adjustment makes a large difference on the results of the liberalization scenario. In particular, the functioning of the labor market appears to make for significant differences in the outcome of tariff cuts. A closure that seems empirically relevant to Tanzania is adopted and several policy scenarios are run. The policy that seems to be the most appropriate for poverty reduction is the one where marketing margins decrease. By contrast, the scenario that assumes significant further unilateral trade liberalization does not seem to produce significant GDP changes, nor does it produce significant changes in household welfare, despite the large degree of liberalization assumed. Hence trade liberalization appears not to be a panacea for growth and poverty alleviation in Tanzania without supply side interventions.