Histogram techniques have been used in many commercial database management systems to estimate a query result size. Recently, it has been shown that they are very effective to support approximation of query processing especially aggregates. In this paper, we investigate the problem of minimizing average errors of approximate aggregates using histogram techniques. Firstly, we present a novel linear-spline histogram model that is more accurate than the existing models. Secondly, we propose a novel histogram construction technique for minimizing such average errors, which is shown to generate a near optimal histogram. Our experiment results demonstrate that the new histogram construction techniques lead to a great accuracy improvement on the existing techniques. Ó 2006 Elsevier B.V. All rights reserved.