Ours ushers have numbered bags for each collection. They put the Saturday and early Sunday collections into the bags, seal them, and put them into a locked cabinet. The counting team, which is separate from the ushers, arrives mid morning, get the bags and count them. There is generally 5 people on the counting team with a minimum of 3 needed to count. All cash is counted twice and the checks are totaled twice. While the team is there the later Sunday morning collections, again in the sealed bags, are brought over by the ushers. Once the counting is done the collection is locked in a deposit bag and two people take it to the bank. Each counting team only counts one weekend a month except for months with 5 Sundays.
I think it’s a pretty good system since there are a lot of checks and balances.