Trade and wages literature asks whether trade or technology has been the major factor behind increases in wage inequality in OECD countries since the 1980s. In this literature, little attention has been paid to how goods market responses to trade shocks affect conclusions. Using an Armington heterogeneous goods trade model we capture demand side effects, and show how trade shocks affecting the price of unskilled-intensive importable goods can be absorbed on the demand side of goods markets, with little or no impact on relative wage rates. No wage impact occurs if the elasticity of substitution in preferences between imports and import substitutes is one. As this elasticity increases, trade plays an ever larger role in explaining wage inequality changes, and as the elasticity goes below one the sign of the effect changes. We present some results of general equilibrium decompositions of total wage change into trade and technology components using UK data. We suggest that since many import demand elasticity estimates are in the neighbourhood of one, there is a prima facie case that goods market considerations further lower the significance of trade as an explanation of recent trends in OECD wage inequality beyond that claimed in the literature.