Clydesdale Bank says its unpublicised £15-a-month Control Account was launched six months ago "for customers who need help with managing their finances".
It was unable to comment on the take-up of the account, but said it was "very much a niche product providing customers with additional choice".
Bank of Scotland charges £10 a month for a similar control account.
Overdraft costs have been under fire at a time of growing pressure on family finances, and last week the Office of Fair Trading revealed the banks are making £2 billion a year from unauthorised overdraft fees.
The control accounts will not process a payment or direct debit if there are not enough funds in the account. On whether that might trigger other interest rate penalties, such as those for missing a credit card payment, a Clydesdale spokeswoman said: "The credit card issuer may impose a late payment fee if a customer was not able to make a payment by another means."
She said the account "gives customers peace of mind by keeping the account in credit or within a pre-agreed overdraft limit".
Clydesdale customers who regularly incur charges could save a lot of money. In the bank's Current Account Plus, a refused payment triggers a painful £35 penalty – or £25 if the damage is less than £10.
Going overdrawn without permission costs £25 a day. If you go into an unplanned overdraft, and then make another payment, the bill is a horrendous £75. For three misdemeanours (or overdrawn days) the charge is £100, for 10 it is £175 and for 21 it is £225.
Will Egerton-Smith at Edinburgh-based budgeting website Money Dashboard commented: "I think it's clear to all now that banks and their services do need to evolve.
"With respect to bank charges, in certain circumstances banks can prove to be more expensive than payday loans.
A better alternative to a control account is the Clear Account (www.clearaccount.com), which does much the same job, but users pay only when they need it, not when they don't."
Clear Account says it can offer a £50 advance for five days for only £2.50, compared with £14.50 from a big payday lender, and a possible £55 charge at a high street bank.
Kevin Lewis, founder of alternative credit provider Frodo Financial, said: "The practice of levying fixed costs on overdraft victims is a penal regime, designed simply to generate higher profits at a time when consumers can ill afford excessive costs."
Lloyds and Bank of Scotland hiked their fees three months ago and the basic fee of £1 a day now doubles when an overdraft hits £2000 and trebles to £3 a day when it hits £3000.
Andrew Pettigrew, a Herald reader and retired BoS banker, commented: "A constant £3000 overdraft would have cost £2 per day, equivalent to 24.3%, but £3 a day is a 50% increase and equivalent to 36.5%.
"For someone being constantly overdrawn by small amounts, even by £1, the cost in percentage terms becomes ridiculous. Even a constant £100 would result in an interest equivalent of 365%."
He said the interest rates were disguised by "dressing the costs up as fees".
A Lloyds Banking Group spokesman said the price change "brought us back into line with the market for larger overdrafts" and affected only 3% of current account customers. "By charging a daily fee, overdraft pricing remains clear and transparent with no hidden charges."
The Halifax arm of the bank, which no longer has any Scottish branches but which does open accounts online, offers new customers a 12-month fee-free overdraft which it says offers a £137 saving for someone with the average £700.
But it then reverts to daily fees. A Lloyds Banking Group spokesman admitted the offer was not available at Bank of Scotland but said: "BoS offers interest and fee-free planned overdraft limits on its range of current accounts."
The no-fee Classic Account allows a buffer of £25, but the big banks tend to reserve their generous buffers for their fee-paying accounts.
HSBC has a "pay monthly" account which charges £15 to ensure the account stays within agreed limits, but it also offers a £50 buffer, text alerts, and access to the bank's regular saver account (maximum interest £65 over a year).
If you are dissatisfied with your bank, now is a good time to look at other options. First Direct is paying a £125 reward for switching to its 1st Account, Halifax will pay £100, and M&S Bank offers a £100 M&S gift card, plus 20% off the store's clothing and homeware for a year.
M&S charges a £15 a month fee, though it offers discount vouchers and a 12-month regular savings opportunity that could earn a maximum £96 interest. It includes an automatic £500 overdraft, with the first £100 free then an interest rate of 15.9%.
First Direct also has a limited 12-month savings opportunity, but here the maximum interest would be £156.
It is also more generous with overdrafts, extending a £500 facility with the first £250 interest-free, then a rate of 14.85%.
Nationwide and Santander do not offer any incentives to switch, and they also charge a basic £1 a day for being overdrawn. But Nationwide's FlexDirect does pay 2% credit interest on balances up to £2500 for the first 12 months, then 1%, while Santander's 123 account pays tiered credit interest and cashback – but costs £2 a month. Santander, however, has regularly failed to shine in customer satisfaction surveys.