Sources providing information about the value of a variable may not be totally reliable. In such a case, it is common in uncertainty theories to take account of this unreliability by a so-called discounting rule. A few discounting rules have been proposed in the framework of imprecise probability theory, but one of the drawback of those rules is that they do not preserve interesting properties (i.e. n-monotonicity) of lower probabilities. Another aspect that only a few of them consider is that source reliability is often dependent of the context, i.e. a source may be more reliable to identify some values than others. In such cases, it is useful to consider contextual discounting, where reliability information is dependent of the variable values. In this paper, we propose such a contextual discounting rule that also preserves some of the interesting mathematical properties a lower probability can have