Can I stop oayments from made before invoices are issued?

[SHFarm]

We only accept payment via PayPal as a courtesy to customers who demand to pay with CC - as this is less than 5% of our customers, paying for a merchant account is senseless, and we cannot afford to eat the fees from either.  The estimated fees are added to those invoices when issued; I'm usually a few cents under, and we absorb it. 
I have a growing problem with those customers sending payment before an invoice is issued in order to stick us with the Paypal fees.  Because it's a down payment-then-balance billing, they know from the DP invoice that we expect them to cover the fees.  When they're told what their balance will be, they're paying it on PayPal without an invoice being issued.  Because our margins are SO small, this is unacceptable. Is there a way to prevent people from sending payment without being invoiced?  The only alternative I can see right now is jacking prices across the board and offering a cash discount...

[sharpiemarker]

@SHFarm 

Recently, it appears that PayPal added Estimates feature so when you quote a client on what their balance would be send an estimate instead and convert it to an invoice somewhere down the road. I've never used this new feature yet but check it out. When you get to the Manage Invoice page, mouseover Create > Create Estimate

Click the Help link on that Manage Invoices page for How to with using Estimates and see if that is a solution you can use. Otherwise, I'd just send a PayPal invoice, ready to be paid and that's when they'll know the balance.