transactions - Why seem to sell and be mafkir chametz?

My understanding is that we do both of the following:

• We (appoint a rabbi as an agent to) sell our chametz to a gentile. This sale takes place the morning of the day before Pesach, before the prohibition of owning chametz kicks in.


• We renounce ownership in our chametz, declaring it ownerless. This also takes place the morning of the day before Pesach, before the prohibition of owning chametz kicks in.

Is seems, then, that whichever of these takes effect first renders us free of ownership of chametz, and whichever we do second therefore has no effect (unless one's acquired chametz meanwhile, an unlikely scenario). So why do the latter act (if, I mean, it has no effect anyway)?