It may seem like you have the upper hand initially, Cooke acknowledged. "But the reality is that they didn't value you in the first place and they're only thinking short term," he said, adding that employers will often be thinking about the costs and risks involved in finding a replacement.
"You have to ask yourself: If they think you're worth that now, why weren't they paying you that earlier?" he said.
Cooke, who is North American director of international recruitment firm Selby Jennings, said that as much as your employer may like you as an individual, once that trust is broken they may become wary of you and your commitment to the firm. They could also use the new information to start considering how they would replace you, giving them an advantage in future negotiations.
"We see it where the trust between manager and the employee has been broken and the majority of people who do take a counteroffer are often on the job market within the next six to 12 months," said Cooke.
Often, agreeing to stay can just mean delaying the inevitable, he noted: "The fact is title and compensation is likely not going to change the things you don't like about your current job. The content and your manager, etc. are linked much more closely to happiness in your role than compensation."