The Supreme Court Wednesday clarified what local governments must do when rejecting plans to build new cellular towers, instructing authorities to promptly provide their reasons to carriers but leaving towns broad discretion over how they do so.

Deutsche Telekom AG ’s T-Mobile South had argued that Roswell, Ga., fell short of federal requirements in 2010 when it sent the company a brief letter denying its request to build an 11-story cell tower in a residential neighborhood, and referred the company to city council minutes to discern the decision’s rationale.

The opinion, by Justice Sonia Sotomayor , rejected T-Mobile’s argument that the city should have provided a written decision spelling out the reasons for rejecting the tower. But it did hold that Roswell erred by taking too long to provide the council minutes for T-Mobile to review.

By a 6-3 vote, the court found that local authorities must provide such materials “at essentially the same time” they deny cell-tower requests, so carriers have an adequate opportunity to decide whether to challenge the decision in court within a 30-day deadline.