However, tenants at other properties may not have checking accounts or may only have pre-paid debit card accounts.

With a non-refundable deposit, it seems awkward to ask for another deposit at renewal time.To Lynn's point, I can definitely see how a tenant could take the mindset that they have "pre-paid" for the right to cause pet damage.

Would you rent your house out to a local 18 year old for two nights during the peak of high school prom and graduation season who may or may not book using a pre-paid visa gift card?  

If you refer to your lease, it will probably tell you that pre-paid rents (in this case they would be post-paid rents) cannot be used for damages or considered as security deposits. 

Here's something to consider- there's a company called Legal Shield (formerly known as Prepaid Legal Services).

Maybe you can install a pre-paid card system to avoid that. 

Disregarding the tenant quality, as an example in Florida prepaid rent must be held in a segregated account and drawn on as the rent comes due.

Can you place the prepaid rent in legal trust? 

I obviously believe in Legal Shield (aka Pre-paid Legal), so I signed up to be an associate for them too.

So follow up on my insurance endeavor.No longer using the big insurance company.Went with a local agent and received the following:home ins on my primary residence @ 300-400 price reductionhome ins on my rental (3unit) @ 200-300 price reductionI'm getting 80-90% back from my prepaid insurance premiums on both propertiesput all my autos (wife's, mom's and mine) @ increase of 200 (oh well)also, got umbrella ins so #dontsuemebroNet Savings of ... $300 / year on the low end.