The Nelson-Oppen method allows the modular combination of quantifier-free satisfiability procedures of first-order theories into a quantifier-free satisfiability procedure for the union of the theories provided that these theories verify some restrictions. In this talk, we will present the Nelson-Oppen techniques for stably infinite, shiny and strongly polite theories, and analyse the relationship between shiny and strongly polite theories in the one-sorted case. We show that a shiny theory with a decidable quantifier-free satisfiability problem is strongly polite and we provide two different sufficient conditions for a strongly polite theory to be shiny. Based on these results, we derive a combination method for the union of a polite theory with an arbitrary theory. Joint work with João Rasga.