The Tiny USB Receiver Is the Reason You Own Two Dead Mice
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Somewhere in your house there is a wireless mouse that works perfectly and cannot be used.
Its receiver is gone. That fingernail-sized nub of plastic went into a laptop, then into a bag, then out at an airport, or it stayed plugged into a machine you sold two years ago. The mouse is fine. It is simply now an ornament, because those receivers are almost never sold separately and are rarely interchangeable between devices.
A design problem with a boring solution
Manufacturers worked this out a long time ago, and the fix is not clever: put a slot in the bottom of the mouse, shaped like the receiver, with enough grip to hold it.
That is the entire innovation, and it is the difference between a mouse that survives being thrown in a bag and one that does not. When you pack up, the receiver comes out of the laptop and clicks into the mouse. It travels with the only object it is useful to.
It also frees a port. On a laptop with two USB slots, a permanently occupied one is a real cost, and people end up leaving the receiver in precisely because they are afraid of losing it, which is how it ends up staying in a machine that gets replaced.

On the compact part
Small mice get recommended for travel, and that is right, but it is worth being honest about the trade. A compact body suits a fingertip grip, where your hand arches over and the mouse moves with your fingers. It is less comfortable for a palm grip, where your whole hand rests on it, because there is simply less mouse to rest on.
Neither grip is correct. But if you spend eight hours a day with your palm flat on a mouse, a compact one will feel cramped by the afternoon, and no amount of portability makes up for that. Small is right for a bag, a second desk, or a smaller pair of hands. It is not automatically right for your main setup.
What this one is
Our compact white wireless mouse has a smooth rounded body, a standard scroll wheel and click layout, and the receiver slot underneath. It is white, which is worth mentioning for the obvious reason: light-coloured mice show hand grime sooner than dark ones, and anyone who has owned a white keyboard already knows whether they care about that.
For battery details and exactly how it connects to your particular machine, check the product page rather than taking my word for it.
See the compact wireless mouse
If you are shrinking the desk generally, the companion piece is why the numpad is pushing your mouse too far right.