In Texas, covenants not to compete are governed by Texas Business & Commerce Code §15.50. I have included a link to the BCC §15 below. You can skim down to §15.50 to read the statute.
Generally, if the non-compete is directly related to the employment, restricted to the employees activities and a reasonable geographical area, and secured through valid consideration (which generally means continued employment or some sort of monetary incentive), it will be enforceable. The most recent precedent from the Texas Supreme Court on this subject is the case of Marsh USA v. Cook. I have included a link to this case below, so you can review it and see that the courts will generally enforce a non-compete agreement which meets the requirements discussed above.
I strongly encourage anyone who is considering a non-compete arrangement to consult an experienced labor and employment attorney and go over the document item by item. There are many good employment lawyers in the Valley, or my firm would be happy to assist you. You can reach me at WFB@BroemerLaw.com.
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As one of my colleagues has already stated, the Texas Business Organization Code Section 15.50 is applicable to your situation. Principally this section:
". . . a covenant not to compete is enforceable if it is ancillary to or part of an
otherwise enforceable agreement at the time the agreement is made
to the extent that it contains limitations as to time, geographical
area, and scope of activity to be restrained that are reasonable and
do not impose a greater restraint than is necessary to protect the
goodwill or other business interest of the promisee."
You should review your non-compete agreement to determine whether there was a certain time length required regarding your employment or whether there was a particular level of employment that you had to reach in order to solidify the agreement. Current Texas caselaw sides with the contract formed (the non-compete agreement) between the employer and employer before your employment departure unless you can demonstrate that the factors listed above will not affect the past employer's business.