Yes, you can–for starters, the leaner the cut of meat, the better. One type of potentially cancer-causing chemical, polycyclic aromatic hydrocarbons, forms when fat from meat drips into the fire and makes flames flicker up–those flames contain PAHs, which stick to meat if they get near. Less fat means less dripping and lower risk for PAHs.
Still, a second possible carcinogen, heterocyclic amines, can form when any cut of meat is cooked at a high temperature. So consider marinating, which can create a barrier between the hot surface and the meat. And scrub leftover crispy stuff off the grill before each use. All that said, if you eat healthfully in general (grill lots of veggies with those lean burgers!), I wouldn’t worry too much about carcinogens in barbecued meat. Sure, there’s a small risk, but I firmly believe that pleasure factors into a healthy life.