The overall least squares solution is found when a complete curve to be fitted consists of two or more submodels, and these have to be joined at points whose abscissae have to be estimated. Under certain standard conditions, each fitted submodel is itself a local least squares solution, and the overall least squares solution can be found quite easily. The exceptions to this rule are studied. The easiest case to handle occurs when a join point** coincides with an abscissa of the given data. In that case it is possible to modify local least squares estimates so that they satisfy an obvious linear constraint (the requirement that the curves do actually join there). If the model is not made up entirely of a mixture of straight lines and constants, we will deal separately with the case where the submodels join together with equal slopes. The solution then requires iterative techniques.