As "Z" indicated, I think many agencies agree that it isn't a requirement, but is a good thing to do. The OCC guidance will tell you that you can pay in any order, but your reasoning shouldn't be to maximize fee income. This tells you that you should justify this. You may have to defend your actions some day.
And from the Texas Dept. of Banking
"Question: Can a bank pay checks that I’ve written in any order it chooses? For example, if several checks are presented for payment in one day, only one of which is more than my balance, can the bank decide to post the larger item first and then the smaller items, even though this would result in more checks not clearing?
Answer: Banks have a right to establish their own policy concerning the order in which they process checks, as stated in the Texas Business & Commerce Code Section 4.303 (b). The Code states that a bank may pay "in any order" and is under no obligation to determine the time of day an item is received. If smaller items are paid first, then there are fewer overdrafts and fewer charges; however, mortgage and rent payments may be returned. Some banks feel that if larger items are paid first, then the most important items are not returned. Payment order should be noted in the deposit contract that customers sign when they open their account."
(Note: the last sentence says "should", not "must".)
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AndyZ CRCM
My opinions are not necessarily my employers.
R+R-R=R+R
Rules and Regs minus Relationships equals Resentment and Rebellion. John Maxwell