The best replacement for compression fitting is solder.

The best alternatives to compression fitting are rated as following:
★★★★★  solder
★★★  barb
★★  sharkbite
★★  flare
★★  threaded fitting
★★  fip
★  flared fitting
★  sweating
★  shark bite
  push fit

Your alternative for compression fitting is not listed? Suggest!
Speaking about compression fitting, one probably shouldn't forget about plastic tubing.

Other search terms related to compression fitting and their ratings are:
★★★★★ plastic tubing
★ valve
shut off valve
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compression fitting
solder
barb