An exclusive poll for ITV Wales suggests that the Conservatives have gained support in the final days of the election campaign.
The results show Labour could match their share of the vote seen five years ago but would still lose seats due to a stronger performance by the Conservatives.
The poll, conducted by YouGov, found that Plaid Cymru are in third place, also matching the support they had in the last Senedd election.
Compared with last month's poll, Labour are up by 1% point in the constituency contest but the Conservatives have gained five percentage points.
Plaid have slipped by four percentage points - and none of the smaller parties have made any progress.
Here are the poll results for the constituencies, with the previous poll results shown in brackets:
Labour 36% (+1%)
Conservative 29% (+5%)
Plaid Cymru 20% (-4%)
Reform UK 4% (no change)
Lib Dems 3% (no change)
Green 2% (no change)
Abolish the Assembly 2% (no change)
The Liberal Democrats can still hope to hold onto a constituency but it is the fact that voters each get two votes in Senedd elections that gives most opportunity to the smaller parties.
As well as the 40 constituency seats, there are 20 regional representatives to choose on Thursday 6 May.
The larger parties' success in the constituencies makes it harder for them to get elected in the regions, making for more unpredictable results.
That happened five years ago when UKIP broke through at that election and although 3% support is a far cry from the 13% achieved in 2016, it is UKIP's best result in recent polls.
But the party that has consistently been showing that it could be in with a chance of winning seats for the first time is the Abolish the Welsh Assembly Party.
YouGov polled a representative sample of 1,071 Welsh voters (aged 16+) for ITV Wales and Cardiff University between 2nd and 4th May.
Watch ITV Wales' 'Election Cuppa' vodcast with Political Editor Adrian Masters and Andrea Byrne as they discuss the latest from the campaign trail.