Savers can now stash up to £15,000 annually in tax-efficient accounts - almost three times the previous cash limit - following the replacement of Isas with new Isas (Nisas) on July 1.

The revamped accounts also allow you to switch freely between cash and stocks and shares - previously there was only one-way traffic from cash to stocks and shares.

You might decide to invest £10,000 into a stocks and shares Nisa and £5000 into a cash account. Or, you might choose to put the whole lot in cash. Any combination is possible. Any money you have already put into an Isa between April 6 and June 30 will count towards the annual allowance for this year.

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As in the past, cash Nisas work like deposit accounts but the interest is tax-free. Stocks and shares Nisas are free from capital gains tax on any profits when you sell. There are also dividend tax advantages to a Nisa for higher-rate and additional-rate taxpayers.

So how do you make the most of the new allowance? Let's say you already have a cash Isa. Most companies allow additional payments, so you can simply top up your existing account. But check the deadline if you have a fixed-rate deal, as many limit top-ups. Clydesdale Bank, for example, permits only one further deposit into its fixed-rate cash Isa - and the deadline is July 31.

You could open a stocks and shares Nisa to soak up the new allowance, or switch to a different cash Nisa - though you will have to transfer the full amount you have deposited since April as you can only pay into one cash Nisa and one stocks and shares Nisa in the same tax year.

The best easy-access cash Isas according to are the Nationwide Flexclusive at 1.75% (though it is open only to holders of its FlexAccount). Or, there's the BM Savings Isa Extra at 1.55%.

Fixed-rate deals tend to pay higher rates, but are not so flexible. Virgin Money tops the table for one-, two- and five-year fixes at 1.76%, 2.1% and 3%. If you want to fix for three years, Clydesdale Bank pays 2.45% (but it is only available through branches). The top four-year fix is from Coventry Building Society at 2.75%, but it does not accept transfers.

There is growing evidence that investors are becoming disillusioned with cash and shifting into shares. A record £2.7 billion was withdrawn from cash Isas in April, according to the Bank of England. And the latest HSBC Savings Map of Britain shows that the average amount in stocks and shares shot up by 40% in 2013, from £4560 to £6391.

Consumers who can cope with some risk - and are prepared to hold their Nisas for at least five years - might want to consider equities.

Jason Hollands, managing director of Bestinvest, an independent financial adviser with offices in Glasgow and Edinburgh, steers more cautious equity investors towards Standard Life's Global Absolute Return Strategies, which aims to deliver positive returns across different market conditions with low volatility. Threadneedle UK Absolute Alpha is another option for investors who want to retain exposure to potential further rises in the UK stock market, but still profit if the market turns sour.

A notch up the risk scale is the Artemis Strategic Assets fund, which invests in UK equities, bonds, cash, currencies and commodities. Or there is the Henderson European Focus fund.

Bestinvest's higher-risk choices include Newton Global Higher Income and Lazard Emerging Markets.

Among ideas from Andy Parsons at The Share Centre is Artemis High Income fund, for investors who want to draw an income. It invests mainly in the UK but can spread worldwide, and has a historic yield of 5.2%.

Watch out for fees, though. Most funds charge an initial fee as well as an annual management fee. Plus, if you seek guidance from a financial adviser, the firm will charge for its services. For example, annual management charges of 2% equate to £300 a year for a £15,000 Isa.

Cash Isas remain more popular than accounts that invest in stocks and shares: Government figures show that four times as many cash Isas were opened in 2012-13. But experts question the wisdom of this when interest rates are so low.

Someone who invested £15,000 in the FTSE All-Share index over 10 years would now have £35,218 compared with £16,582 if they had left their money in the average UK savings account, according to Fidelity Personal Investing. That's a difference of £18,636.