Delivery of packages by drones to homes and workplaces is faster and cheaper than delivery by van and hence has significant potential. That potential can only be realized if delivery by drones is safe. In particular, such drones must not pose a threat from in-air drone-drone collisions. To determine how serious the drone collision problem might be, we: 1) focus on a situation where they would be maximized, New York City, and 2) investigate the “do nothing” alternative, in which the drones do nothing to avoid collisions. Such drones, lacking a collision-avoidance capability, are “dumb” drones, and will have a much higher collision rate than “smart” drones, which do have that capability and will ultimately be deployed. The do nothing alternative is useful for determining the extent to which a collision-avoidance capability is needed. The dumb drone collision rate is found to be unacceptably high. Actual smart drones to be ultimately deployed must therefore have a highly effective collision-avoidance capability to bring collision rates close to zero. The needed effectiveness is quantified.