In this paper we analyze the bias in a general linear least-squares Gift Items parameter estimation problem, when it is caused by deterministic variables that have not been included in the model.We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known.We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its Cases essential properties and some numerical results on an applied example.