Is it possible to disable a trigger momentarily but for just one table.

For example I have table, TableA with an on insert, update and delete trigger. I also have a table B with the same triggers but they only affect certain columns in table A.

I now have an update query that uses both tables. I know the updates in table A need to fire the triggers but the updates in table B definitely do not need to fire the triggers. So I would like to disable those triggers until the updates are done.

Is this possible? I'm using MySQL 5.1