Constant elasticity of substitution (CES) demand for monopolistically competitive firm-varieties is a standard tool for models in international trade and macroeconomics. Inter-variety substitution in this model follows a simple share proportionality rule. In contrast, the standard toolkit in industrial organization (IO) estimates a demand system in which cross-elasticities depend on similarity in observable attributes. The gain in realism from the IO approach comes at the expense of requiring richer data and greater computational challenges. This paper uses the data generating process of Berry, Levinsohn and Pakes (1995), BLP, who established the modern IO method, to simulate counterfactual trade policy experiments. We use the CES model as an approximation of the more complex underlying demand system and market structure. Although the CES model omits key elements of the data generating process, the errors are offsetting, allowing it to fit BLP-based predictions closely. For aggregate outcomes, it turns out that incorporating non-unitary pass-through matters more than fixing over-simplified substitution patterns.