Kehoe and Perri (2002) show that a two-country business cycle model with endogenously incomplete markets helps to resolve the "international comovement puzzle" (. Baxter, 1995) and the "quantity anomaly" (. Backus et al., 1992, 1995). We claim that a similar performance can be achieved without resorting to market incompleteness. We show that a model with complete markets driven by productivity shocks alone can account for the "international comovement puzzle". Our model features time nonseparable preferences that allow arbitrarily small wealth effects on labor supply. It matches the data by predicting (i) positive cross-country correlations of investment and hours worked; (ii) realistic cross-country correlations of consumption. It reduces the gap between international correlations of output and consumption, but fails to change their order. Unlike models with restricted international markets, ours show little sensitivity to the parameterization of the forcing process.