Pensions have become increasingly difficult to understand, especially for those in final salary schemes and higher earners.
This Budget has added further traps for the unwary.
As expected, the amount that can be saved in a pension free of tax over the course of a lifetime is to be reduced from £1.25m to £1m from April 2016.
If your pension savings are more than £1m by that date, or you expect that what you have already saved will have grown to more than £1.25m by the time you take your pension, it is likely that you will be able to protect the funds you already have, as long as you do not put any more into the pension.
This is known as "fixed protection". HM Revenue and Customs (HMRC) are expected to publish details of this shortly.
The amount that can be saved in a pension tax-free each year - the annual allowance - has been set at £40,000 since April 2014.
There will be changes to this system too.
At present, you can contribute up to £40,000 a year into a personal pension scheme.  If you have a "defined contribution" employer scheme, the total of employer and employee contributions must not exceed £40,000.
The position is more complicated if you have a final salary scheme. Each year you are in the scheme, the value of the pension you will receive on retirement increases.
The tax law assumes that you need a fund of 16 times that increase in order to pay the pension. So if you are a member of the pension scheme for a year, and your pension would go up by £2,000 as a result, tax law treats you as having increased your pension fund by £32,000.
This increase must not be more than £40,000, or you have to pay tax on the excess.
However, if you have not used your annual allowances in previous years, you can carry forward the unused amounts from up to the last three years.
Under the new rules announced in the Budget, this £40,000 allowance will be reduced for those whose total income is above £150,000.
In working out whether your income is above £150,000, you need to include the value of any pension contributions you make, any pension contributions made by your employer, and the increase in value of any final salary scheme over the tax year. This is called "adjusted income".
For every £2 of adjusted income you have over £150,000, your annual allowance will be reduced by £1. The maximum reduction is £30,000, leaving an annual allowance of £10,000.  So once your income is over £210,000, there is no further reduction.
If you have unused annual allowances from earlier years, these can be carried forward in the usual way and added to your tapered annual allowance.
If your taxable income - after pension contributions and other reliefs - is £110,000 or less, then these rules will not apply.
In April, there was a major overhaul of pensions, allowing people to take out some of their pension in cash - possibly to buy cars or pay for holidays.
If you have taken money out of your pension using the new "flexible access" provisions, existing laws reduce your annual allowance to £10,000.
So you do not have a £40,000 annual allowance any more.
This does not mean that you escape these new tapering rules.  If you only have a £10,000 annual allowance, and your adjusted income is more than £150,000, the £10,000 allowance is tapered to zero.  If you have income of £210,000 and have flexibly accessed your pension, you therefore have a zero annual allowance.
The current pension regime gives tax relief when you put money into a pension. This pot grows largely tax-free, and you are taxed when you take it out, apart from a 25% tax free lump sum.
If your employer pays into the scheme, or funds a final salary pension, there is no employee or employer National Insurance Contributions (NICs) on the value of these payments or benefits.
Among the Budget papers is a consultation document which suggests replacing this long-standing system. Instead of tax and NICs relief on contributions, pension saving would be made out of after-tax income, as with the Individual Savings Account (Isa) system. When the money was taken out, it would be tax-free, under these proposals.
The Budget also announced the abolition of "pension input periods".  These are complicated but critical in setting how much tax relief you get on your pension contributions, and people can get caught out by getting their timing wrong.
The changes are highly technical. Before you make a contribution to your pension, you should find out whether they make a difference to your position.  The government have published some helpful examples to guide people.
This Budget not only chipped away at the pension tax regime, but also suggested that the entire edifice might be pulled down and replaced.