The performance of three rules for dealing with outliers in small samples of sizenfrom the normal distributionN(μ, σ2) are investigated when the primary objective of sampling is to obtain an accurate estimate of μ. It is assumed that at most one observation in the sample may be biased, arising from eitherN(μ +aσ, σ2) orN(r, (1 + b)σ2). Performance of each rule is measured in terms of “Protection”, the fractional decrease in the Mean Square Error (MSE) obtained by using the rule when a biased observation actually is present in the sample. Although numerical results have been obtained forn≤ 10 when σ2is known, computational difficulties have prevented evaluation of protections when σ2is unknown except whenn= 3.