A new goodness-of-fit test for the two-parameter Weibull distribution or extreme-value (smallest element) distribution with unknown parameters is presented in this paper. The test statistic is based on similar principles used in the derivation of the well known W test for normality. The test statistic is simple to compute and requires no table of constants. Percentiles and power for a wide variety of alternative distributions are estimated via simulation. A comparison of the proposed test with the Mann-Scheuer-Fertig procedure shows that the power of the test for the former is as high or higher than that for the latter.