Small sample power and efficiency are computed for the one sample Wilcoxon and normal scores tests for normal shift alternatives. A recursive scheme is given which reduces the problem of power computation permitting investigations up to sample size $N = 10$. Local efficiencies for the two nonparametric tests are computed for small samples using the values of the normal scores statistic. In addition, efficiencies for large shifts are obtained by comparing the exponential rate of convergence to zero of the type two error.