There exist many application classes for which the users have significant flexibility in the quality of output they desire. At the same time, there are other constraints, such as the need for real-time response or limit on the consumption of certain resources, which are more crucial. This paper provides a combined language/compiler and runtime solution for supporting adaptive execution of these applications, i.e., to allow them to achieve the best precision while still meeting the specified constraint at runtime. The key idea in our language extensions is to have the programmers specify adaptation parameters, i.e, the parameters whose values can be varied within a certain range. A program analysis algorithm states the execution time of an application component as a function of the values of the adaptation parameters and other runtime constants. These constants are determined by initial runs of the application in the target environment. We integrate this work with our previous work ...