Object and relational technologies are grounded in different paradigms. Each technology mandates that those who use it take a particular view of a universe of discourse. Incompatibilities between these views manifest as problems of an object-relational impedance mismatch. In this paper we propose a conceptual framework for the problem space of object-relational impedance mismatch and consequently distinguish four kinds of impedance mismatch. We show that each kind of impedance mismatch needs to be addressed using a different object-relational mapping strategy. Our framework provides a mechanism to explore issues of fidelity, integrity and completeness in the design and implementation of existing and new strategy choices. Our framework will be of benefit to standards bodies, tool vendors, designers and programmers as it will provide them with new insights into how to address problems of an object-relational impedance mismatch both at the most appropriate levels of abstraction and in the most appropriate way.