Recently, there is an increasing interest in programming models of real-time systems and approaches of flexible scheduling for dealing with situations of transient overloading, which can occur in non-deterministic environments. This paper presents the (p+i, k)-firm approach that can be seen as a combination and generalization of imprecise computing [3] and of deadline (m, k)-firm [7]. This approach extends the (m, k)-firm concept allowing a task to execute in an imprecise way, obtaining better results than a deadline missing. The approach seeks to establish a compromise between avoiding temporal failures and maximizing the quality (cumulative value). A battery of tests was developed to evaluate the approach and its capacity to reduce the probability of dynamic failures and to obtain a smooth degradation in overload conditions.