Get a copy of the agreement you signed. Closely reading the non-compete agreement you signed can give you a better idea of the interests the company seeks to protect and what you need to stress in asking for a release.

Make sure that you actually signed the agreement, and that a corporate representative with power to bind the company also signed the agreement. Without the signature of both parties, a contract such as a non-compete agreement is not binding on either party.
If the non-compete agreement in your HR file wasn't signed (either by you, by a corporate representative, or both), a court won't enforce it. This can give you great leverage in negotiations to get a release from the agreement, because essentially there is no agreement.
Assuming the agreement was properly signed, next study the provisions detailing your employer's responsibilities. If any of those things didn't happen, or if they changed, the agreement is likely no longer enforceable. The same holds true for any designations of your employment or your role in the company.
For example, if you signed a non-compete agreement when you were a sales representative, but you are now a sales manager, that original non-compete agreement may be unenforceable – unless you signed a new agreement for your manager position. Put simply, although the agreement bound you as a sales representative, it may not bind you as a sales manager.
The key for courts is whether your employment relationship changed. Any change of job duties, authority, or compensation may invalidate your old agreement. Document Job Changes.
You also should carefully read the scope of the agreement. The job you want to take may not, in fact, violate the non-compete agreement. For example, if you have a non-compete agreement that prohibits you from working for another company that uses "the same or similar technology" as your old employer, and the new employer actually uses different technology, the non-compete agreement probably doesn't cover your new job – even if the two companies provide similar services or are involved in the same industry.
Consider what your job at the company entailed. Non-compete agreements exist to protect trade secrets, or to protect business relations. The company has you sign a non-compete agreement because they're worried you'll take their clients to your new company, or use the trade secrets you learned and use them to benefit the new company. However, if you didn't have any direct relations with clients, and didn't learn any trade secrets, the non-compete agreement probably isn't enforceable against you.
For example, some companies just require every employee to sign a non-compete agreement, regardless of their role in the company. If you were hired as a receptionist for one company, and you've now been offered a position as an executive assistant in another company, it is unlikely you have any trade secrets or client relationships that you could take to the new company.
A non-compete agreement, like any other contract, must be supported by valid consideration. This means your employer must have provided you with some additional benefit or compensation in return for your signature on the non-compete agreement. If you weren't provided any additional benefits, or if you were promised a bonus or other compensation that you never received, that would invalidate the agreement.
In some situations, simply making your continued employment contingent on your signing of the non-compete agreement constitutes valid consideration. This could be the case if, for example, your employment was categorized as "at-will" employment, and you didn't sign any other employment contract stating otherwise.

Darius & Company NATIONWIDESTAFFING & RECRUITING AGENCY

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Darius & Company

NATIONWIDE
STAFFING & RECRUITING AGENCY

Serving the International Ocean & Air Freight Forwarding,
Logistics, & Supply Chain Industries.

FOR SALES, OPERATIONS,
& DISCREET EXECUTIVE RECRUITING.

STAFF RECRUITING SINCE 1986