The least-squares method in system identification leads generally to biased parameter estimates. A conceptually simple modification is to estimate the bias and to compute compensated parameter estimates. When white output noise is the only disturbance this principle (compensated least squares, CLS) can readily be used to obtain consistent estimates. The main purpose of the paper is to investigate the accuracy of the parameter estimates obtained when the CLS method is used. It is proved that the estimates are asymptotically gaussian distributed. An explicit expression for the covariance matrix is given. It is also shown that a commonly used instrumental variable method gives (asymptotically) better accuracy than the compensated least-squares method.