Methods for indirect comparisons and network meta-analysis use aggregate level data from multiple studies. A very common, and closely related, scenario is where a company has individual patient data (IPD) from its own trial, but only has published aggregate data from a competitor's trial, and an indirect comparison of the treatments evaluated in these two trials is required. Matching-Adjusted Indirect Comparison (MAIC) has been developed for this situation, where we use the available IPD to adjust for between-trial imbalances in the distributions of observed baseline covariates between the two trials. We extend the current MAIC methodology, where we compute the weights that satisfy the conventional method of moments and result in the largest possible effective sample size (ESS). We show that the approach proposed by Zubizarreta in a previous study can be used for this purpose. We derive a new analytical result that shows why this alternative approach provides a larger ESS than a conventional MAIC. We also derive a new formula for the maximum ESS that can be achieved, even when permitting negative weights, when adjusting for one covariate. This can be used as an easily computed new metric that quantifies the difficulty in adjusting for covariates.