To answer the question, if you hold the bird's neck between two fingers and with your thumb force the head to the side with enough force to break its neck it will die instantly. Taking care to stop when you feel the neck break avoids the head separating, together with most of the commotion if a "civilian" sees the process. With practice, this can be done with the arm hanging down by your side so it is not obvious that you are dispatching the bird, and you can still look for more doves. In some jurisdictions, it is better not to shood a bird while standing on the right of way and post it on social media. Also, picking a Roebuck up from someone else's Revier might be frowned upon.
Mike