With rates on bank and building society accounts generally being driven down rather than up by competitive pressures, savings experts say supermarkets are offering some worthwhile deals.
A savings card scheme announced by Asda last week has been described as a "no brainer" by one savings specialist.
The bonus it offers is the equivalent to a savings account paying 5.21% gross, or 4.17% net.
Other conventional savings accounts offered by high street stores have featured regularly in the best buy tables according to Moneyfacts, the financial data providers.
Asda's savings card is aimed at people who want to put money aside to cover the cost of Christmas rather than running up credit card bills or worse.
It allows customers to save up to £144, for which Asda will pay a tiered bonus if the money remains on the card until November 18.
Anna Bowes, director of SavingsChampion.co.uk, said: "For those who shop in Asda this is a no brainer – especially if you can put £144 on the card.
"You can earn the bonus even if you add the money just before the bonus payment date – but even if you were to save regularly, the bonus on the maximum amount of £144 offers a great return.
"It's less appealing for lower balances, nevertheless it is still good value."
By comparison, rates on ordinary bank and building society savings accounts have been falling in recent months despite no change in the Bank of England base rate.
The average best buy easy access account is now paying 2.79%, down from a high of 3.22% in July.
Falling savings rates have been attributed to the Government's Funding for Lending scheme, designed to stimulate the economy by making cheaper loans available to firms and individuals.
Savers appear to be suffering because it has taken the pressure off banks and building societies and they no longer need to pay higher rates to attract money from smaller savers.
Ms Bowes said: "It means that, as soon as a savings provider's account appears at the top of the best buy tables, they are withdrawing it and replacing it with one that pays a lower rate, because they don't want to have to pay more than they need to to attract deposits.
"At the beginning of the year they were leapfrogging over each other to appear at the top of the tables."
On the bright side, Sylvia Waycot of Moneyfacts has pointed out that savers are still able to get considerably more than the base rate, which has been at 0.5% for the last three and a half years.
Five years ago, when the base rate was 5.75%, the average no-notice account paid just 4.08%.
There are still many savings accounts now paying less than base rate, such as Nationwide's e-Savings account which pays 0.45%, the Clydesdale Bank's 40 Day Notice account paying 0.25% and the Dunfermline Gold Account, which pays just 0.1%.
Savers in these accounts could give their returns a real boost by switching to a supermarket's savings account.
Tesco Bank, for example, offers a pretty competitive easy access account paying a rate of 2.60%, including a bonus of 1.35% for 12 months.
Even more attractive is Tesco's one year fixed rate bond, the best for lower balances, which offers 3.20% gross on a minimum deposit of £2000.
Sainsbury's Bank has also just launched new one to five year Fixed Rate Saver accounts.
The rates are 3% gross for 1 year, 3.10% gross for 2 years, 3.25% gross for 3 years, 3.35% gross for 4 years and 3.50% gross for 5 years.
These accounts can be opened with a minimum of £5000 up to a maximum of £50,000.
However, the first savings option for every saver each year should be to make maximum use of a cash ISA allowance to receive interest with no tax deducted.
Up to £5640 can be deposited in a cash ISA in the current tax year.
Somewhat surprisingly, Tesco does not offer a cash ISA. But two of the best ISA deals available are from Marks & Spencer and Sainsbury's.
M&S Bank has the market's top easy access cash ISA paying 3% on £100 – but it is cutting it to 2.75% from December 11. Sainsbury's Bank is still paying 2.8% on £500.
Anna Bowes points out that the additional benefit is that both are straightforward clean accounts with no short-term bonuses or restricted withdrawals.
Cash Isa Sainsbury's 2.8%
M&S 2.75% (from Dec 11)
Fixed Rates Sainsbury's 3% to 3.5%
Easy Access Tesco 2.6% inc bonus
Savings Card Asda 5.21% equivalent