We develop a new approach to estimating flexible demand models with exogenous supply-side shocks. Our approach avoids conventional assumptions of exogenous product characteristics, putting no restrictions on product entry, despite using instrumental variables that incorporate characteristic variation. The proposed instruments are model-predicted responses of endogenous variables to the exogenous shocks, recentered to avoid bias from endogenous characteristics. We illustrate the approach in a series of Monte Carlo simulations and an application to the demand for Medicare Advantage insurance plans.