In the regression model y"t = @a + @bt + @e"t is found that when the residuals @e"t follow a first-order stationary Markoff process with zero mean and autocorrelation coefficient @r, - 1 < @r < 1, the greatest lower bound for the efficiency of the least-squares estimator of @b (relative to the Gauss-Markoff estimator) over the interval 0 @? @r < 1 is .753763. This compares with a greatest lower bound of .535898 for the relative efficiency of the Cochrane-Orcutt estimator of @b.