To analyse the schedulability of conditionally guaranteed budgets (CGBs) in the context of fixed-priority preemptive scheduling (FPPS), we present a so-called cognacglass algorithm (CGA). CGBs have been conceived in the context of software video processing for consumer terminals to exploit the relative importance of applications. CGBs are similar to normal budgets, but are only conditionally guaranteed. This paper presents the schedulability analysis of CGBs under FPPS, based on both best-case and worst-case analysis techniques. We show that because both techniques are used, it is not straightforward to base the analysis on a critical instant. We therefore have to investigate multiple phasings of budgets during the analysis, for which we present a socalled cognac-glass algorithm. We derive that it suffices to consider only a subset of so-called dominating values for the phasing, which improves the efficiency of our algorithm. Given our analysis, we evaluate the effectiveness of CGBs, and conclude that CGBs are particularly useful for software video processing. Finally, we briefly compare our approach for CGBs with existing analysis techniques for hierarchical FPPS, and illustrate that best-case analysis techniques and a CGA can reduce the inherent pessimism in these existing techniques.