A framework, called α-acceptability, is proposed for evaluating alternatives to the usual least squares estimates of regression coefficients. An estimate is defined to be α-acceptable if it is in the usual (1 - α) 100% confidence region, Estimates which are α-acceptable for large values of α, such as .99 (corresponding to a 1% confidence region) are viewed as statistically indistinguishable from the usual estimates and, in a sense, simply rounded off. Applications to subset selection, ridge regression, and a class of minimax procedures are discussed and illustrated with an example.