Adding regressors to obtain efficiency

It is well known that in standard linear regression models with independent and identically distributed data and homoskedasticity, adding irrelevant regressors® hurts (asymptotic) efficiency unless such irrelevant regressors are orthogonal to the remaining regressors. But we have found that under (conditional) heteroskedasticity irrelevant regressors® can always be found such that one can achieve the asymptotic variance of the generalized least squares estimator by adding the irrelevant regressors® to the model.