Our site is too fast, please slow it down!

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Said no client ever 🙄

I have seen an example of this, though not necessarily what you might think. The new code was so much more efficient that some of our processes that run parallel, began colliding. Go a quick fix we ended up putting in a quick wait.
While the customers didn't necessarily notice the speed improvement, they definitely noticed when the system would lock up.

I wrote a web program that made calls to the white pages api. Problem was, my code queried faster than white pages could handle so I had to bog the code to slow it down!