The conventional model of on-line scheduling postulates that jobs have non-trivial release dates, and are not known in advance. However, it fails to impose any stability constraints, leading to algorithms and analyses that must deal with unrealistic load conditions arising from trivial release dates as a special case. In an effort to make the model more realistic, we show how stability can be expressed as a simple constraint on release times and processing times. We then give empirical and theoretical justifications that such a constraint can close the gap between the theory and practice. As it turns out, this constraint seems to trivialize the scheduling problem.