GREENWICH, Conn. (CBSNewYork) — Burglaries are a constant battle in one of the wealthiest towns in America.

Greenwich recently increased police patrols following a series of high-profile burglaries in the wooded northern part of town.

There is some good news.

A federal warrant has been issued for a suspect in at least one case and residential break-ins are down slightly for the year, Police Lt. Kraig Gray said.

But residents need to remain vigilant and take precautions, especially as the holidays approach, Gray said.

He is urging residents to lock up, set the alarm, get motion sensor lights and use timers that alternate throughout the house.

Packages left on doorsteps are also easy targets for thieves and Gray is suggesting a few tips to keep residents from becoming victims.

“Anything that keeps a package secure and not left out in the open,” Gray said. “Whether it is scheduling a delivery, having it delivered to your work so that you can sign for it directly, have a neighbor pick it up.”