A new point estimator for the AR(1) coefficient in the linear regression model with arbitrary exogenous regressors and stationary AR(1) disturbances is developed. Its construction parallels that of the median--unbiased estimator, but uses the mode as a measure of central tendency. The mean--adjusted estimator is also considered, and saddlepoint approximations are used to lower the computational burden of all the estimators. Large--scale simulation studies for assessing their small--sample properties are conducted. Their relative performance depends almost exclusively on the value of the autoregressive parameter, with the new estimator dominating over a large part of the parameter space.