This paper introduces a technique for meter placement for the purpose of improving the quality of voltage and angle estimates across a network. The proposed technique is based on the sequential improvement of a bivariate probability index governing relative errors in voltage and angle at each bus. The meter placement problem is simplified by transforming it into a probability bound reduction problem, with the help of the two sided-Chebyshev inequality. A straightforward solution technique is proposed for the latter problem, based on the consideration of 2-$sigma$ error ellipses. The benefits of the proposed technique are revealed by Monte Carlo simulations on a 95-bus UKGDS network model