I've expressed my dissatisfaction with my current company multiple times for them to change their tune. Since current company still have not changed how they behave, I've decided to leave and made it known to my managers today.
When they learned I had received an offer, they asked if I was expecting a counter offer. I let them know that if they decided to counter I would be happy to consider it but my mind has been made up that the right decision is to leave.
If your mind is really made up for leaving, there is no reason in playing with the fire and risking your perspective employer to doubt your commitment.
If, as you say, it's the company tune that motivates you to leave, it is not an higher salary that will accommodate that. You are wasting time (yours, your current manager's, your future manager's) just to fiddle. If this comes to surface it won't praise your attitude.
