Deleted messages still viewable

When you delete a message on your iPhone or iPad, you think it is deleted right? Well, that may not be the case. I just noticed today that when I delete text or iMessages that if I go to the spotlight search on my iPhone and type in a keyword or phrase, it will show a list of deleted messages and snip-its from messages that are no longer on my phone. It does not show all deleted messages so I'm assuming that this is related to some type of caching but I don't like the thought of someone being able to see past messages that I thought were deleted. Does anyone know of a way to stop this from happening? Any input would be great.

Cheers