Jisas replaced Child Trust Funds (CTFS) a year ago this week and were touted as the Coalition Government's flagship savings scheme for children.
They are open to the six million children under the age of 18 who do not already qualify for a CTF, and work in a similar way. The annual limit on both accounts is £3600 and any gains or interest are tax free.
The child cannot touch the money in either a Jisa or a CTF until he or she is 18.
Anyone can pay into a Jisa but there is no contribution from the Government.
If your child already has a CTF, you are stuck with it. You can continue to make payments into the account and you can usually switch to another CTF if you are unhappy with the performance of your current fund. But you cannot transfer the money to a Jisa.
Danny Cox, head of advice at Hargreaves Lansdown, a leading independent financial adviser, says: "The choice of CTFs is now limited and the costs can be high, putting CTF customers at a disadvantage. It makes absolute sense to merge CTFs with Jisas. It would also be relatively easy and cost the Treasury almost nothing."
Jason Hollands, managing director of Bestinvest, one of the UK's biggest independent financial advisers, says: "The time has come for the Government to provide a way out for children stuck in zombie CTF accounts."
Voters agree, according to a recent poll by women's financial website SavvyWoman.co.uk. It found 95% of those polled support the merger of the old and new accounts.
There are 75 CTF providers on the Government website, but almost a quarter are Welsh credit unions and almost half provide no information on CTFs on their own websites, according to Bestinvest. If you take out a Jisa, on the other hand, there are thousands to choose from.
Charges for CTFs are also higher than the equivalent Jisa, eating into returns. For example, you would pay an annual management fee of 1.5% if your CTF was invested in the Scottish Widows Investment Partnership (Swip) Foundation Growth fund through The Children's Mutual.
But you can invest in the same fund through Hargreaves Lansdown's Vantage Junior Isa for an annual charge of 0.07%, plus a £2 fee.
If you put in the full £3600, you would pay charges of £54 a year for the CTF, compared with £26.52 for the Jisa.
Tom Stevenson, investment director at Fidelity Worldwide Investment, says: "Children with CTFs are being discriminated against. One of the main attractions of Isas is their simplicity but this benefit is reduced as long as the CTF and Junior Isa schemes run in parallel."
The confusion might partly explain the relatively slow take up of Jisas. Official statistics indicate that just 72,000 accounts were opened in the 2011-12 tax year, representing its first five months.
But Mr Cox says: "When Jisas came on to the market last November, many providers were not up and running. But more are coming on stream so we expect awareness of the accounts to grow.
"We should also remember that money is tight for many households so the lack of any contribution by the Government could also be an issue."
There are two types of Junior Isa. A cash Jisa works just like an ordinary savings account but the interest is tax free. They are available from most banks and building societies and the current top deal is Nationwide's Smart Junior Isa with a variable rate of 3.25%. Nationwide was also offering the top rate back in November 2011, although it was then a slightly lower 3%.
Stocks and shares Isas are more risky because they invest in the stock market. However, most experts favour stocks and shares over cash.
Mr Hollands says: "Cash is the worst place to park your money for the long term, as its value will slowly be eroded by inflation. In fact cash typically halves in real value every 14 years.
"Children with money in these accounts can expect to receive a derisory amount on their 18th birthday, which will have little utility beyond a round of drinks".
Advisers recommend funds run by experienced managers.
Mr Cox says: "The principles of picking funds for a Junior Isa are the same as for an 'adult' Isa. Pick two or three areas where you believe there are decent prospects for the long term and then choose good quality managers and stick with them."
The top performing fund since last November is the Neptune UK Mid Cap with a return of 39.6%, according to Moneyfacts.
Gillian Liddell already has an adult Isa but it was the arrival of the junior version which tempted her to start saving for daughter Amelie, 19 months. Unlike the regular Isa, the Jisa locks your money in until the child is 18 but Ms Liddell, an accountant from Paisley, says that is one of the attractions. "The temptation would be there to use it sooner, plus the fact you are building up your investment." She adds: "I am hoping she would listen to us when the time comes and do something sensible with it." She opted for the Jump Junior Isa, which feeds the money into the global Witan Investment Trust, because of the potential for long-term returns.