Skip running trigger during cascade delete?

Question

I have a legacy application where I have two tables X and Y. Table Y has a trigger that performs an action automatically on delete. There is also a foreign key with cascade delete defined between X and Y (such that entries in Y are deleted when X is deleted).

Is there any way to have the trigger NOT run during a cascade delete?

The only way I currently know that this could be done is to create a package level variable to use as a flag that the trigger would check to determine if it should run. I would then change the value of the flag in my stored procedure before and after running the delete on table X.

I was hoping to find something a bit cleaner where you could simply tell oracle not to execute the trigger if it is a cascade delete.