In this paper we present a new method for combining linear least squares estimates obtained from independent data sets. A bank of Square Root Information Filters (SRIF) is used to generate these "local" estimates as well as their corresponding smoothing coefficients which can be merged after each predictive step to obtain globally optimal smoothing coefficients. Additionally, the merging algorithm recursively computes a global information vector and square root information matrix which can be merged with their local counterparts to obtain globally optimal values. Globally optimal smoothed estimates and covariances are obtained from a backwards recursion using either the smoothed estimates and covariances directly [1] or a data equation Square Root Information Smoother (SRIS) [2] which uses the globally optimal Dyer-McReynolds smoothing coefficients as input. A major advantage of our approach over a decentralized covariance approach is its ability to add effects of the a priori initial estimate covariance and process noise to the results obtained with these effects omitted. In the covariance based case, the effects have to be subtracted (after they have been included twice). An additional feature of the approach is that it is not even necessary to reprocess the data when the a priori initial state covariance and process noise variances are changed. This is especially attractive when one is trying to "tune" the filter for problems with large amounts of data.