We present a new method for computing core universal solutions in data exchange settings specified by source-to-target dependencies, by means of SQL queries. Unlike previously known algorithms, which are recursive in nature, our method can be implemented directly on top of any DBMS. Our method is based on the new notion of a laconic schema mapping. A laconic schema mapping is a schema mapping for which the canonical universal solution is the core universal solution. We give a procedure by which every schema mapping specified by FO s-t tgds can be turned into a laconic schema mapping specified by FO s-t tgds that may refer to a linear order on the domain of the source instance. We show that our results are optimal, in the sense that the linear order is necessary and the method cannot be extended to schema mapping involving target constraints.