The formula proposed yesterday for determining maintenance contributions is more generous to absent fathers, so it is less likely to impoverish them or their second families. Previous settlements, involving the transfer of property, will now be taken into account. Flexibility, discretion and an appeal system are at last built in.
These changes mainly comprise concessions to men - in particular middle-class men - some of whom will now escape altogether the attentions of the agency. There is still a case for a more generous approach to allow women to keep at least some of their benefits even when a former partner increases his contribution.
Rather than choosing this option, Mr Lilley has offered a lump sum to women who return to work. This will be a help only to those women who can find jobs.
But the political purpose of his thinking is clear. The Government needs to neuter largely male political opposition to the agency, in order to allow it to settle down and do the job which most people want it to perform. Yesterday's reforms at last create the possibility that the founding of the CSA will eventually be seen for what it is - an important piece of social engineering.
The CSA's true significance lies in the fact that it is making men think differently about their responsibility towards their children.
Margaret Thatcher, the inspiration behind the CSA, coined the phrase "Parenthood is for life". Women have always recognised the truth of this statement. But some men have deluded themselves about what it means to be a father. Many of them have imagined that they are free to ignore the consequences of their own actions. No more.
As such, the creation of the CSA bears comparison with the legalisation of abortion and the facilitation of divorce. In itself, the agency may only be concerned with the financial relationship between parents and their children. But its activities may eventually also lead to absent fathers playing a larger emotional role in the lives of their estranged children.
Those who first specified the detail of the CSA perhaps imagined that they were involved simply in trying to save money for the Treasury. Ironically, the ferocity of the political contest which has taken place over their botched work has raised the profile of the debate about parental responsibility and so made an impact on British culture well beyond the individual families with which the agency has dealt.
So although the main benefits of yesterday's changes went to men, they will not be the ultimate winners. By ensuring the CSA's survival, the concessions will in the long run play an important part in modernising the ground rules which govern the workingsof the British family.