This paper defines the preliminary test estimator (PTE) of the univariate normal mean under the original as well as the Edgeworth size corrected Wald (W), likelihood ratio (LR) and Lagrange multiplier (LM) tests. The bias and mean squared error (MSE) functions of the estimators are derived. The conflicts among the biases and the MSEs of the PTEs under the three original and the size corrected tests have been obtained. It is found that instead of the original W, LR and LM tests, the use of the Edgeworth size corrected W, LR and LM tests in the formation of the PTEs reduces the conflict among the biases and MSEs of the estimators remarkably.