This paper determines the most appropriate ways to model diffusion and jump features of high-frequency exchange rates in the presence of intraday periodicity in volatility. We show that periodic volatility prevents conventional tests from accurately identifying the frequency and location of jumps. We propose a two-stage correction for periodicity that improves the properties of the test statistics. The most plausible model for 1-minute exchange rate data features Brownian motion and finite activity jumps but not infinite activity jumps. Brownian motion and Poisson jumps account for 85% and 15% of the quadratic variation, respectively, and these proportions appear to be stable through time. The low proportion of jump variation is consistent with the high liquidity and high reliance on public information of currency markets compared to stock markets. The empirical results also indicate that microstructure noise biases but does not unduly impair the statistical tests for jumps and diffusion behavior at the 1-minute frequency.