Holders of maturing Tessas can roll over all or part of their capital with their existing provider, or transfer to a different one without penalty. Either way they have up to six months to do so. No one need rush to decide. But in order to ensure that the new account remains tax-free, anyone who does want to transfer rather than roll over more than pounds 3,000 needs to get a certificate of entitlement from the original supplier.
Tessas are not necessarily the best place to invest or even re-invest your money. Over the last five years investors would have done better on a corporate bond Pep (if they had existed), and on a personal equity plan invested in UK shares. But Tessas are super-safe and that is what matters most to many investors.
In general the bigger providers offer lower rates, relying on their name and reputation. The smaller providers - who ran away with the prizes for the best returns on first generation Tessas - are once again offering the best rates of return.
But interest rates offered on day one are not the only thing investors need to watch. Some rates are fixed for the full five years while others are liable to change. Rates vary according to the amount invested, and some are restricted to existing customers only. Others - like the Halifax, for example - tweak the basic rates with a maturity bonus which is payable at the end of five years. Another variation on the rates theme is to offer an escalating rate over five years.
Some institutions have opted for loyalty bonuses payable only to customers who have rolled over an existing Tessa, and a small number - including Lloyds Bank, Kleinwort Benson and Birmingham Midshires - offer optional returns which are linked to future stock market performance.
Most accounts allow holders to draw interest during the life of the Tessa but some either insist the interest accumulates or withhold the maturity bonus if holders want to draw it.
Investors must also watch out for transfer penalties, which like mortgage redemption penalties effectively lock customers in once they have opened their new account. Penalties can go as high as 180 days loss of interest on fixed-rate Tessas, if customers try to find a better rate elsewhere later on. Straightforward withdrawals are not penalised, although they do lose their tax-free status.
The highest rate on a variable rate Tessa of pounds 9,000 - the maximum sum which can be reinvested - is 8 per cent from Northern Rock, which initially offered 7.25 per cent before Christmas and then decided to lift its rates higher to establish itself as the market leader.
Elsewhere the best rate is 7.75 per cent from Cheltenham & Gloucester, which offers the same rate on amounts as low as pounds 1,000 - so long as they are renewing existing C&G Tessas. The transfer fee is also only pounds 30. National Counties pays 5 per cent on pounds 1,000 rising to 7.5 per cent on pounds 9,000 with a 90 day interest penalty. Bradford & Bingley offers 5.75 per cent on minimum sums of pounds 500 rising in steps to 6.75 per cent on pounds 9,000, but a maturity bonus of 0.75 per cent a year is also payable for investors who last the course, and only one month's notice without penalty is required to transfer. Birmingham Midshires offers 7.25 per cent on sums as small as pounds 3,000 but wants 180 days interest from transfers. Alliance & Leicester offers 7.25 per cent, but imposes 60 days loss of interest on transfers.
Natwest Bank pays the best rate among the clearing banks with 7.19 per cent compound on sums from pounds 5,000 upwards if interest is not drawn - but it charges 180 days interest on transfers. and does not allow additions after the first year.
Bristol & West pays 4.9 per cent on sums as small as pounds 500 rising in steps to 7 per cent on pounds 9,000 , and combines a maturity bonus of 1 per cent on the first year investment with a similar sum as a loyalty bonus for existing customers. Three months notice is required and three months loss of interest is charged on transfers.
Darlington Building Society offers 7.5 per cent to existing Tessa holders on sums as small as pounds 1 - but docks 60 days interest from transfers. Monmouthshire pays 7.6 per cent to roll-over customers on as little as pounds 1 and charges just one month's interest on transfers.
Some of the bigger players offer much less generous rates. Abbey National for example is offering just 6 per cent on sums of pounds 3,000 rising to 6.6 per cent on the maximum roll-over fund of pounds 9,000, while the Halifax is offering just 5.9 per cent, with a terminal bonus of 2.5 per cent if it is held to maturity, bringing the overall rate up to 7.4 per cent.
The best fixed rates on offer include 7.64 per cent fixed on pounds 9,000 from Northern Rock, but the penalty for transferring is 180 days interest plus a pounds 30 fee. West Bromwich offers 7.55 per cent fixed with 28 days notice and 180 days loss of interest to deter subsequent transfers.
Bradford & Bingley offers 7.5 per cent fixed, but one month's notice plus 180 days loss of interest is required for transfers. Barclays Bank pays 7.5 per cent fixed on amounts of pounds 7,500 upwards with a month's notice and a variable fee for early withdrawals. Sun Banking offers a 7.5 per cent fixed rate carrot on maximum amounts, and a 180 notice plus 180 days loss of interest stick on transfers.
Yorkshire Building Society offers 7.3 per cent to existing customers with the full amount to roll over with an 180 loss of interest in years one and two, dropping to 90 days thereafter. Only 7 per cent is paid by Abbey National's fixed rate account, but the withdrawal fee is only pounds 20.
Britannia Building Society offers 7.25 per cent fixed on the full pounds 9,000 to its existing Tessa holders and 7.15 per cent fixed to new investors but there is no transfer penalty and both get a 1 per cent bonus after a year. The Derbyshire offers 7.2 per cent fixed on full roll-overs from existing customers, but levies 180 days interest on transfers.
Compiled with the help of data analysts Moneyfacts and financial advisers Johnson Fry.