The pound;16 million fund is being targeted at schools where a fifth or more of pupils are entitled to free school meals (FSMs), with the aim of raising the achievement of the most disadvantaged children.
But Janet Ryder, shadow education spokesperson, said using FSMs to share out the money was unfair. She called for another indicator, possibly based on previous educational attainment, to be used instead.
But Jane Davidson, education, lifelong learning and skills minister, this week defended the allocation of the Raise fund (raising attainment and individual standards in education).
The Assembly government also announced that schools which hit the 20 per cent FSM requirement, when new figures for 2006 come out later this term, will get Raise funding. Schools which have already been allocated funding based on 2005 data will not have it taken away if their FSM entitlement has fallen.
Ms Ryder said schools with small canteens, and not enough FSM pupils would be the biggest losers. "FSMs are not a good enough indicator of who needs this money most - they are economic indicators but not educational ones,"
she told the Assembly's education, lifelong learning and skills committee.
The Welsh Local Government Association has already expressed "regret and considerable dismay" over the way the grant is being handled. But Ms Davidson said inspection body Estyn used FSMs as a poverty indicator.
FSMs average 18 per cent in Wales, and around 614 schools are expected to benefit from Raise.