Observational studies assessing causal or non-causal relationships between an explanatory measure and an outcome can be complicated by hosts of confounding measures. Large numbers of confounders can lead to several biases in conventional regression based estimation. Inference is more easily conducted if we reduce the number of confounders to a more manageable number. We discuss use of sufficient dimension reduction (SDR) summaries in estimating covariate balanced comparisons among multiple populations. SDR theory is related to the dimension reduction considered in regression theory. SDR summaries share much with sufficient statistics and encompass propensities. A specific type of SDR summary can wholly replace the original covariates with no loss of information or efficiency. Estimators with minimal expected loss can be based on these SDR summaries rather than all of the covariates.