A nonprofit housing finance corporation convinced a Texas appeals court Thursday to dissolve insufficiently specific temporary injunction orders preventing the organization from acquiring tax-exempt property in three cities.

Texas’s Housing Finance Corporations Act allows local governments to sponsor nonprofit organizations for coordinating affordable-housing facilities. Fort Worth, Arlington, and Haltom City, Tex., convinced a trial court that they suffered irreparable injury from a housing nonprofit they didn’t sponsor claiming tax exemptions within their borders.

However, the Texas Court of Appeals, Second District said the injunctions granted to Arlington and Fort Worth were “woefully deficient” of information.

The order granted to Haltom …