The best replacement for neat is up.

The best alternatives to neat are rated as following:
★★★★★  up
★★★  on the rocks
★★★  straight
★★  sloppy
★★  straight up
★★  messy
★★  sloppy people
★★  scansnap
★★  rocks
★  neet
★  evernote
★  dirty drink
★  dirty martini
★  fujitsu
★  soccer am
★  susy
★  paperport
  neater
  snapscan
  dirty
  tidy
  beat
  dirty drinks
  shoeboxed
  doxie
  luggage works
  nair
  genie
  scruffy

Your alternative for neat is not listed? Suggest!
Speaking about neat, one probably shouldn't forget about little bit of luck lyrics.

Other search terms related to neat and their ratings are:
★★★★★ little bit of luck lyrics
★ little bit of luck
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Google Trends

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neat
up
on the rocks