Nearly 90% of construction workers have now signed-up to the new BESNA agreement, despite continuing strike action by union Unite.
Figures from employers show that 88% of those workers who were asked to sign and return their contracts have done so.
The mass sign-up comes despite a vote by Unite members at Balfour Beatty Engineering Services for strike action over plans to replace the JIB pay and conditions deal with the new BESNA agreement.
Seven leading contractors who are introducing the new agreement with the Heating & Ventilating Contractors' Association (HVCA) gave their employees BESNA contracts.
Blane Judd, HVCA's chief executive, said: "The companies have always communicated the facts about BESNA to their employees and it's good to see that this information has been so well received. We hope that Unite will also now acknowledge the facts, cease making false claims about pay cuts and deskilling and stop threatening unjustified industrial action."
The seven companies working with HVCA to introduce BESNA are Balfour Beatty Engineering Services, Crown House Technologies, Gratte Brothers, NG Bailey, Shepherd Engineering Services, SPIE Matthew Hall, and T Clarke.
Any workers who have still not signed and returned their contracts are being contacted by their employer to discuss any concerns that they may have.