Limits are being set on counter withdrawals and internet transfers at two major UK banks.
Basic account customers will not be allowed to take out amounts of less than £300 from the counter at Alliance & Leicester from 1 July.
And, from August, HSBC customers may be required to make a telephone call to confirm internet transfers to people to whom they rarely send money.
The bank said the move was designed to tackle fraud.
A number of banks and building societies have made changes to their counter services in an attempt to cut queues at branches.
From 7 June, Nationwide Building Society customers with cash cards who want to withdraw amounts of less than £100 will have to use a cash machine. The change will not apply to people with debit cards, or those who still use a passbook.
Now Alliance & Leicester has announced that, from 1 July, the counter withdrawal minimum for customers with the basic bank account will rise from £250 to £300.
The change aims to bring the bank brand in line with other banks in the Santander group, which already have the £300 level set.
The 278 branches of the Alliance & Leicester will be renamed as Santander later this year. More than a thousand former branches of the Abbey and Bradford & Bingley banks are already undergoing the name change.
In a separate move, HSBC said some of its customers may be required to make a telephone call for security checks for rare cash transfers made on the internet.
From 1 August, payments to somebody who has not previously received a transfer from the account for 13 months may be blocked until the call is made.
Payments for utility bills or regular direct debits will be unaffected.
However, if, for example, somebody wants to pay a friend who they have not paid money to over the previous 13 months, then the payment will be blocked until the payer calls telephone banking or visits a branch.
The upper limit on such payments remains the same at £10,000 a day.