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You can certainly make a short sling with a 6" bury. Do you also want it to be full strength? If so, you should probably test your short sling to see just how strong it is.
I think there is no way such a sling will be full strength. The bury will begin to slip out long before you reach max tension, and when it does, the brummel will tighten into a tiny and very weak knot (about 1/3 the strength of the rope). The bury, now even shorter than before, must carry 2/3 of the load or the rope will break. If the bury is tapered, so much the worse, because its effective length has been reduced.
Essentially you are betting that a 6-inch bury in 3/4 Tenex is enough to give you 2/3 the strength of a full-length bury of over 30 inches. Not a bet I would want to make.
But if you only care to have a 1/3 strength rope, you should be fine.
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Very interesting info Moray, thanks!
What about the short bury beeing lock stitched, so it cant pull out? How much bury "does it need" to maintain 2/3 of a total one?