While some companies in Houston may accept applicants with broken leases, it's important to note that acceptance policies vary from one property management company to another. Broken leases can be a red flag for landlords and property managers, and they may be more selective when considering such applicants. Here are some strategies and considerations to increase your chances of finding a rental property if you have a broken lease:

1. Provide an Explanation: Be upfront about your broken lease and provide a reasonable explanation. Landlords may be more willing to consider your application if you can demonstrate that the issue leading to the broken lease is no longer a concern.

2. Offer a Co-Signer: If your credit or rental history is a concern, having a financially stable co-signer (such as a family member) can boost your application's credibility.

3. Larger Deposits or Prepaid Rent: Some landlords may be more amenable to accepting applicants with broken leases if they pay a larger security deposit or several months' rent in advance.

4. Rental References: Provide strong rental references from subsequent landlords who can vouch for your responsible tenancy since the broken lease.

5. Professional Property Management Companies: Consider renting from larger property management companies or corporate-owned apartment complexes, as they may have more standardized application procedures and may be more open to applicants with broken leases.

6. Search for Listings Online: Websites and apps like Zillow, Apartments.com, and Rent.com allow you to search for rentals, and some even include filters for "second chance" apartments, which may be more lenient with broken leases.

7. Engage with Apartment Locators: Houston has a vibrant apartment locator service industry. These professionals have insider knowledge about available rentals and can help you find properties that may be willing to work with your specific situation.

8. Build or Repair Your Credit: While not an immediate solution, working on repairing your credit and demonstrating responsible financial behavior over time can significantly improve your rental prospects.

9. Be Patient and Persistent: Finding a rental with a broken lease may take time, so be patient and persistent in your search. Keep applying to various properties and following up with property managers.

10. Legal Assistance: In some cases, if your broken lease was a result of landlord misconduct or if there are issues of habitability, you may want to seek legal advice. If you believe your broken lease was unjust, consult with an attorney.

Remember that there is no one-size-fits-all solution, and acceptance policies can vary widely. Your best approach is to be transparent about your situation, be prepared to offer additional assurances, and explore a variety of options when searching for a new rental property in Houston.