offer, and that you actually received another offer the very same day from a different, attractive company. Both offers are worth consideration. Would you be willing to increase my base salary to $__________? (think big--+10%?). Be prepared to say yes to the stable one if the hit it. If only the less favorable company bumps, than start over pondering about things.

You will be surprised how you can improve your lot in life with respectful negotiation.