The basic Tessa allows you to save up to pounds 9,000 over five years with the interest rolled up free of all tax. The average return from a maturing Tessa has been just under pounds 11,500. When your first account matures, you have six months to decide whether to invest the full pounds 9,000 capital in a Tessa mark two.
There are now several types of Tessas on offer, whether for maturing accounts or new savers.
Usually the highest interest rates apply to the larger investments. It can also depend on where you live - as small, local building societies often offer the best interest rates but only to those who reside in their catchment area.
Your capital is not at risk in a Tessa - other than from inflation - but you should think about the level of certainty you are looking for.
The first choice is between a variable and a fixed interest rate plan. If you feel - as most financial experts do - that interest rates are likely to rise, then a variable rate will be more attractive. Most are linked to bank base rate and currently offer 7-7.25 per cent.
Fixed-rate Tessas, linked to money market rates, offer around 7.5 per cent. Some institutions offer a fixed rate for the first, and even second year, with variable rates thereafter.
To lock savers in, some providers offer a relatively low rate, typically 6 per cent a year, with a bonus of 1.5 per cent on the total at maturity. Others offer a tiered rate where, the larger the amount being saved, the higher the rate of interest.
A further complication comes from those offering escalating rates. Usually for second Tessas, a typical example will be 5.75 per cent in year one, 6.5 per cent in year two, 7 per cent in year three, 8 per cent in year four and 9 per cent in the last year.
Recently, a handful of providers have introduced a new, higher risk account. These are equity-linked schemes. They usually guarantee a low rate of interest plus an additional amount which depends on the rise in stock market values.
One example offers 4 per cent simple interest plus the percentage rise in the FTSE 100 over the five-year saving period. Another, from Abbey National, offers 1.15 per cent interest for each month that both this index and Wall Street's S&P 500 rise, but nothing if they fall. Over most five-year periods, stock markets usually rise. But there are no guarantees that this will always be the case.
If the local building society does not offer an attractive scheme, choosing between the different types of Tessa will depend on your view of the future. Historically, interest rates are low and most experts think they will rise during the course of the next five years. This means that variable interest rates are more attractive while equity-linked Tessas are for those who think the stock market will continue booming.
But always remember, most Tessas can be transferred if you change your mind. This means that they can be switched later on to a higher fixed rate if interest rates rise.
The usual penalty for this is a loss of between 30 and 90 days' interest, higher for fixed rate and equity-linked schemes, or up to pounds 30 in administration fees. But some of the high-performance accounts quote such high charges for transfers that you will inevitably be better off staying put