Or "...shoot, kill..." if the method should be noted in the headline.
I see the main problem with "Police shoot dead gunman" as the ambiguity. I don't imagine most North Americans saying something like "Police shoot gunman dead who took hostages," but it'd be less ambiguous and less susceptible to ridicule.
I could say the same for "Police shoot dead a gunman..." and wonder if "a" isn't there simply because headline writers seem to have retained a habit, from the recent days of print, of compressing the language in headlines.
I don't imagine most North Americans saying something like
I was referring to SkyDancer's post #4 and forgot to refer to it in my finished post:
Its the dumb way Europeans use the English language. Even the UK Daily Mail does it.