We demonstrate use of bivariate area-level models to improve small area estimates from one survey by borrowing strength from related estimates from a larger survey. Specifically, we demonstrate the potential for borrowing strength from estimates from the American Community Survey (ACS), the largest U.S. household survey, to improve estimates from smaller U.S. surveys, without using regression covariates obtained from auxiliary sources. Applications presented show substantial variance reductions for state estimates of health insurance coverage from the National Health Interview Survey, and for state estimates of disability from the Survey of Income and Program Participation, when modeling these jointly with corresponding ACS estimates. A third application shows substantial variance reductions in ACS one-year county estimates of poverty of school-aged children from modeling these jointly with previous ACS five-year county estimates of school-age poverty. Simple theoretical calculations show how the amount of variance reduction depends on characteristics of the underlying data. For our applications, we examine three alternative bivariate models, starting with a simple bivariate Gaussian model. Since our applications involve modeling  proportions, we also examine a bivariate binomial logit normal model, and an unmatched model that combines the Gaussian sampling model with the bivariate logit normal model for the population proportions.