Your non-compete is negotiable even after you have signed it and spent years working for your employer. Non-competes are negotiable because they are only enforceable in limited circumstances, expensive to enforce and the court will most likely edit the time and scope of your non-compete anyway after your employer has spent considerable money to try and enforce it.
Your ability to negotiate the terms of your non-compete depends on a variety of leverage factors including the circumstances of your departure, whether you are receiving compensation for the time you are restricted, the type of work you engaged in, your value to your employer and your relationship with the company. A good time to re-negotiate the terms of your non-compete are in conjunction with a severance negotiation.