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Using other webbing width (wider or narrower)
Wider webbing than designated on the lineGrip plate may never be used, under any circumstance!
Even if you could squish it inside, either rolling up the edges, or folding the webbing, it will tend to flatten out with rising tension, potentially damaging itself and the lineGrip by forcing the levers apart.
Narrower webbing is less an issue, as long as you ensure it is properly centered between the plates, and reduce the load as the webbing approaches 16mm, which is the minimum approved width.
Use MWL 12kN for 20mm and MWL 8kN for 16mm as rule of thumb,