Caterham, HRT and Marussia have all failed to score since joining the grid at the start of the 2010 season, but given the great potential for driver errors and attrition at Monaco, they have a bigger chance of doing so here than at any other track.
Although Caterham driver Heikki Kovalainen stopped short of predicting points, he believes that if his team can get its cars to the finish there is hope.
"I'm not really thinking about points yet," said Kovalainen when asked if he was optimistic.
"This is an unusual race and something is more likely to happen here than on a normal race weekend. Making the finish is the priority for us.
"Because the track is shorter, the gaps between the cars might be shorter but I would still expect us to be in the same position as previously.
"I don't think we'll gain positions because of the nature of the circuit, but it's more about circumstances.
"It might be difficult for everyone to do the optimum and that gives us a better opportunity."
HRT's Pedro de la Rosa is optimistic that his team will be more competitive in Monaco because of the slow track configuration.
"It's a race of opportunities and that is why, when you are not in a competitive team, you look forward to coming to Monaco," de la Rosa said.
"If you drive well and work on the suspension and achieve a good balance, you can be more competitive than elsewhere.
"After Barcelona, we know what type of corners are hurting us most [higher-speed ones]. And there are not so many of them in Monaco."
Charles Pic, whose Marussia outfit is the best-placed of the three teams in the constructors' championship, is also optimistic.
The Frenchman, a winner on the streets of Monaco in both Formula Renault 3.5 and GP2, is anticipating a more competitive showing as he continues to impress in his rookie campaign.
"Monaco is a little bit special because it doesn't allow any mistakes from the drivers, so I think it can be a really interesting weekend for us," said Pic.
"It's interesting to see our pace on a type of circuit like that. It is quite different to other circuits."