WordNet sense 1 (an official report (usually sent in haste)):

communique, despatch

WordNet sense 2 (the property of being prompt and efficient):

expedition, expeditiousness

WordNet sense 3 (complete or carry out):

complete, discharge, discharge

WordNet sense 4 (kill intentionally and with premeditation):

hit, murder, off, remove, slay, polish off, bump off

WordNet sense 5 (the act of sending off something):

shipment