Computerized voting, with all the networking and such, but with an optically and manually readable ballot form printed out by the machine after you punch your selections. This form, after being inspected by the voter, goes straight into a normal ballot box at the polling site under the same security routines that ballot boxes have been under for decades.

The boxes of paper ballots are not counted, but simply locked away like ballots are now after elections.

If there is an argument about the computer results, the paper ballots can be hauled out and run through normal counting processes, both optical reading and manual recount if necessary. For the vast majority of elections, they'd stay in storage, and people would still have the advantage of the quick returns on electronic voting.