I am in a rather delicate situation. I've been working in a startup company for 2 years. My position and environment were very fulfilling but I can't say the same about my salary. After some talks with my boss (and his apathetic reaction), I've decided to end my contract. Wasn't long I found a new position in a high reputation firm. Feeling pretty determined, I signed a contract at the firm, that binds me to start working there in August.
After seeing that I wasn't bluffing, my old boss decided to throw me a counteroffer that includes a higher salary (higher than the new firm's offer) and stock options so that I'd stay. After thinking about it for sometime, I've decided to stay.
How should I approach the new firm for terminating my contract? The problem is, that they might have me bought plane tickets for a business trip. I would also prefer no further negotiations because I've made my mind.
Can someone give me some tips on diplomacy for this situation?
-- Edit
The country I'm from is Lithuania.