Thousands of men who are missing out on up to €40 per week in their pension payments will not benefit from the proposed 'fix'.
Social Protection Minister Regina Doherty announced a move to a 'total contributions' model that will use people's total PRSI contributions and not their yearly average to decide their entitlement.
A HomeCaring Credit has also been introduced that will benefit those, mainly women, who spent up to 20 years outside of the workforce to raise children.
The changes will kick in from March 30, 2018, but the first payments will not be made until early 2019.
While the focus has largely been on the women who have lost out on money to date due to the anomaly, thousands of men are also at a disadvantage under the new system but they are not likely to benefit from the incoming changes.
Around 15,000 men - 37pc of those affected - have been hit by the revised band structure.
It has emerged a significant proportion of these men are unlikely to benefit from higher payments.
Fianna Fáil welfare spokesman Willie O'Dea, who has pushed for changes over the past six months, conceded that Ms Doherty's changes "were a step in the right direction". But he insisted there were too many snags - and it would have been better to revert to the system before the changes in 2012 which created the anomaly.
"Not many men will qualify. I know it was perceived as primarily a problem with women pensioners [but men are also losing]," he said.
Ms O'Doherty estimated some 30,000 pensioners who had retired since 2012 will see an increase in their pensions but last night the department said it was not possible to give exact figures until those who are receiving less had explained the gaps in their contributions.
A spokeswoman conceded that "people with homemaking/caring periods pre-1994 are expected to gain the most", while those with gaps but no significant caring periods are less likely to see any gain.
Age Action - which also pressed for the reversal of the 2012 legislation - has also expressed disappointment that not everyone who has seen their pension reduced will benefit from higher payments.
"The changes will benefit those who left the workforce to care for family members, which is a positive step forward, but it is not going to do anything for people whose time out of the workforce was not related to care giving and many of them will be men," said Justin Moran, Age Action's head of advocacy.
"By acting to address the concern of people who were out of the workforce for caring reasons, the department has not addressed the people who were out of the workforce because they took a summer job before college, or were self-employed."
Limerick City TD Mr O'Dea said the delay in people actually getting money, and the risk that people now just a few years short of retirement would end up being much worse off, were also serious problems.
"Will anybody get paid in the lifetime of this Government at all? Beneficiaries will qualify from this March but their money will not be paid out until some time in 2019," Mr O'Dea told the Irish Independent.
He welcomed the proviso allowing existing pensioners to stay with the old regime if they risked losing money on the new system.
But he warned the move to the new regime may seriously hit those coming up to retirement in the next three to five years as the pension qualification thresholds will rise.
People affected by the "bonkers" pensioner anomaly won't be able to avail of the higher rate as the Department of Social Protection does not yet have an adequate IT system to deal with the issue, Regina Doherty has said.
Thousands of pensioners who are missing out on up to €35 a week because of an anomaly in the system are to be restored to a higher rate from March – but they won’t get the money until 2019.