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Is 4mm enough to hit the mark or is that too short? I can't find any literature on the ideal depth.

I have the Autoject Ei, but with the 31 gauge 5/16" syringe only about 4mm protrudes from the end of the long barrel. The short barrel works and I have used the autoject 2 in the past, but both of those barrels allow for too much wiggle room which seems to lead to a lot of misfires.

I saw that another franktalk member mentioned using the 1/2" needles with the long barrel, but as far as I can tell those are only available in 29 gauge.

I have my own reasons for not wanting to inject manually (essential tremor).

I've only injected manually with 8mm or 12.7mm needle length, depending on what side and where along my length I've chosen. Four millimeters usable length would never work for me. Autoject users will give you a better answer.

You need the 1/2" needles for the autoinjectors. The 5/16" is too short, you lose too much length in the contraption. The 31 gauge is probably too thin too. Try the 29 gauge. Maybe the 30 gauge but they might bend.