Pirelli has warned F1 teams that they cannot allow the pressures to drop below the prescribed minimum limit after cars leave the pits during the Italian GP.
The minimum tyre pressures are measured by the car's telemetry as they leave the pitlane, and that information is recorded by the Pirelli engineers who work with each team.
Any anomalies are then picked up by the FIA.
There is clearly a suspicion that teams have found ways to meet the legal requirement as the car leaves the pits, but then run on track with slightly lower and thus more favourable pressures, which in turn aid car performance.
Pirelli says that if that is found to be the case the team concerned will be given higher minimum starting pressure figures.
In the letter, seen by Motorsport.com, Pirelli's Mario Isola told the teams: "Our prescriptions about minimum starting pressures are based on the assumption that running pressures are higher than starting ones.
"These are the historical values we've seen, and we therefore need you to respect this in order to operate the tyres safely.
"If we find, during any session, that your stabilised pressures are equal to or lower than the starting pressures, we will give higher starting pressures limit to your team, as agreed with FIA."
Temperatures being watched
One way to promote a pressure drop on track is to have very high blanket temperatures, and Pirelli has underlined that the temperature numbers are being watched: "I also remind you to respect the maximum temperature for blankets as we will ask FIA to random check the values."
Teams are also believed to be trying to get around the pressure requirements via both set-up and operational means.
It has been suggested for example that drivers have been leaving the pits with new tyres and passing the minimum pressure requirement.
They have then returned to the pits and the mechanics have reduced the pressures before the car heads out again to do a proper run.
"We need to be sure that the running pressure is in-line with the starting pressure," Isola told Motorsport.com.
"I fully understand that the teams need to find performance, that is clear. On the other side we have to be sure that the tyres are working in the right way. It's always a balance between the two.
"When we find something that is not what we want, the tyre is not operating in the range we want we need to be sure to come back to a situation is under control.
"For me it is not correct to say that people are cheating. They are trying to find the room in the regulations to do something that is allowed because it is not forbidden.
"If we realised that this new idea has a negative impact on the tyre, we need to react, and to police it. They've found some grey areas where they can work at the limit, that's all."
Meanwhile, one team insider told Motorsport.com that pressures could drop dramatically during the course of Sunday's race: "The car set-up can promote a reduction in pressure, but the biggest factor is tyre wear.
"As the rubber thickness reduces the tread temperature decreases and this cools the air inside, and pulls the tyre pressure down.
"This is what happens during a long stint e.g. Ferrari in Spa. And it's what's going to happen tomorrow when everyone attempts a one-stop strategy."