A situation recently came up in my weekly game where a PC who had just discovered a new magic item after a series of encounters took a short rest to identify the magic item's properties. Per the DMG, this is all that is needed to identify a magic item's properties so there's nothing wrong with that.
The magic item required attunement, so I told him it was useless to him until he attuned with it. He asked for the rules on attunement and I told him it requires another short rest. No further short rests came up during that adventuring day, so the party decided to set up camp.
The question came up, "Can I attune during a long rest?"
I determined based on the following excerpt from the DMG that the answer to that question is no:
Some magic items require a creature to form a bond with them before their magical properties can be used. This bond is called attunement...
Attuning to an item requires a creature to spend a short rest focused on only that item while being in physical contact with it (this can't be the same short rest used to learn the item's properties). This focus can take the form of weapon practice (for a weapon), meditation (for a wondrous item), or some other appropriate activity. If the short rest is interrupted, the attunement attempt fails. Otherwise, at the end of the short rest, the creature gains an intuitive understanding of how to activate any magical properties of the item, including any necessary command words...
So, naturally, the player said, "Okay, I take a short rest just before the long rest."
Something about this really doesn't sit well with me but I can't find a reason in the rules for not allowing this. Obviously it's not the intended usage of rests (short or long) based on the adventuring day, but I really didn't have any good rationale behind disallowing the short-then-long rest.
For reference, I have included the pertinent rules relating to short rests and long rests below.
A short rest is a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds...
A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours. A character can't benefit from more than one long rest in a 24-hour period...