This paper reconsiders the nonlinearity test proposed by Koenda (Koenda, E. (2001). An alternative to the BDS test: integration across the correlation integral. Econometric Reviews20:337-351). When the analyzed series is non-Gaussian, the empirical rejection rates can be much larger than the nominal size. In this context, the necessity of tabulating the empirical distribution of the statistic each time the test is computed is stressed. To that end, simple random permutation works reasonably well. This paper also shows, through Monte Carlo experiments, that Koenda's test can be more powerful than the Brock et al. (Brock, W., Dechert, D., Scheickman, J., LeBaron, B. (1996). A test for independence based on the correlation dimension. Econometric Reviews15:197-235) procedure. However, more than one range of values for the proximity parameter should be used. Finally, empirical evidence on exchange rates is reassessed.