In the area of process mining, decomposed replay has been proposed to be able to deal with nets and logs containing many different activities. The main assumption behind this decomposition is that replaying many subnets and sublogs containing only some activities is faster then replaying a single net and log containing many activities. Although for many nets and logs this assumption does hold, there are also nets and logs for which it does not hold. This paper shows an example net and log for which the decomposed replay may take way more time, and provides an explanation why this is the case. Next, to mitigate this problem, this paper proposes an alternative way to abstract the subnets from the single net, and shows that the decomposed replay using this alternative abstraction is faster than the monolithic replay even for the problematic cases as identified earlier. However, the alternative abstraction often results in longer computation times for the decomposed replay than the original abstraction. An advantage of the alternative abstraction over the original abstraction is that its cost estimates are typically better.