It is well known that under fair conditions linear regression becomes a powerful statistical tool. In practice, however, some of these conditions are usually not satis?ed and regression models become ill-posed, implying that the application of traditional estimationmethodsmayleadtononuniqueorhighlyunstablesolutions.Addressingthis issue,inthisarticleanewclassofmaximumentropyestimatorssuitablefordealingwith ill-posed models, namely, for the estimation of regression models with small samples sizes affected by collinearity and outliers, is introduced. The performance of the new estimators is illustrated through several simulation studies.