A majority of people believe Wales should have either a full law-making and tax-varying parliament, or be an independent nation, a poll has found.
Roland Rat and Teddy dressed up by Ysgol Gymraeg Rhyd y Grug pupils
A St David's Day poll for BBC Wales also suggested that 60% of people think the assembly government should have the most influence over Welsh life.
But 80% did not think £67m should have been spent on the new Senedd building.
The BBC commissioned poll by ICM Research spoke to over 1,000 people across Wales over three days last week.
According to the poll's findings, public opinion in Wales seems to be moving in favour of devolution and an increasing majority of people want that process to accelerate significantly.
Back in 1997, when the Labour government began to implement the devolution process, almost 40% in Wales were firmly against the creation of any kind of assembly, while fewer than 20% wanted a full law-making parliament.
However, according to the St David's Day poll, these figures have now been completely reversed - with just 20% wanting to abolish the assembly, 21% wanting to keep the status quo, 39% want a more powerful parliament (with full law-making and tax-varying powers), and 16% in favour of independence.
This suggests that 55% of people in Wales - a clear majority - now want significantly more devolution.
Interestingly, the poll also shows stronger support from women for a parliament, and a clearer advocacy of abolition among men.
The poll also reveals that 60% believe the Welsh Assembly Government should have the most influence over Wales, compared to just 21% who think the UK Government in Westminster should have the most influence.
Asked about their perception of the current situation in 2006, only 40% thought the UK Government has the most influence - despite the fact that it still retains all primary legislation and taxation powers.
Moreover, given that back in 2001, nearly 65% said the UK Government had the most influence over Wales, then this suggests a further erosion in how people view the UK Government's role in life in Wales.
The pollsters also asked people about their feelings about the new assembly building.
Despite all the publicity surrounding the Senedd over a period of many years, 23% said they were not aware that the assembly had a new home at all.
Of those questioned, 56% felt it was right for the assembly to have a new building, with 38% against.
But when it was pointed out that the building cost £67m, a massive 80% said that paying this amount for a new building was not worth it.
A significant 58% said the name Senedd is an appropriate name for the new building - with the highest level of support amongst people aged between 18 and 34.
However, almost a third said that the name was inappropriate, providing some more ammunition for both sides in the ongoing debate about the name of the new building.