Escaping the 1/24 plateau
The "1/24 plateau" refers to the usually frustratingly lengthy period of getting the final product once you have two x4 31 Pokemon of the correct nature in the daycare. Giving a power item to one parent (and the Destiny Knot to the other) so the flawless IV the other parent lacks is always inherited can modify this process to speed it up slightly. With a power item, you have a 1/10 chance (1/5 of all the write IVs being inherited, 1/2 of the other parents IV being inherited) of a receiving a x5 IV parent, albeit with the wrong nature. From here, you can substitute in the x5 IV wrong nature parent for either parent and continue breeding, the wrong nature parent holding a Destiny Knot and the correct nature parent holding the Everstone. The chance of receiving a flawless egg is now 1/12. This doesn't save a great deal of effort, and will have you breeding an extra set of competitively useless parents in the process, but narrowing down your chances can prove useful if you're frustrated with your x4 IV parents taking too long. It's a case of whether you want to work with two higher chances or one lower one.
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