In this article we introduce a new procedure for estimating population parameters under inequality constraints (known as order restrictions) when the unrestricted maximum liklelihood estimator (UMLE) is multivariate normally distributed with a known covariance matrix. Furthermore, a Dunnett-type test procedure along with the corresponding simultaneous confidence intervals are proposed for drawing inferences on elementary contrasts of population parameters under order restrictions. The proposed methodology is motivated by estimation and testing problems encountered in the analysis of covariance models. It is well-known that the restricted maximum likelihood estimator (RMLE) may perform poorly under certain conditions in terms of quadratic loss. For example, when the UMLE is distributed according to multivariate normal distribution with means satisfying simple tree order restriction and the dimension of the population mean vector is large. We investigate the performance of the proposed estimator analytically as well as using computer simulations and discover that the proposed method does not fail in the situations where RMLE fails. We illustrate the proposed methodology by re-analyzing a recently published rat uterotrophic bioassay data.