In many applications, approximate results are often acceptable, due to the nature of computations. The authors describe a system called Concord which supports an imprecise computation scheme. For each procedure, a supervisor is used to record values of the intermediate results. When a procedure terminates either voluntarily or involuntarily, its supervisor returns the best, albeit maybe still imprecise, result. The application can check if the result is acceptable using special handling routines. The authors discuss the issues of system support for Concord and define the basic features required. Also discussed are some advanced features which extend the capability of the system.