YAPB - Yet Another Parametrized Box, this one segmented 

This is a completely parametric, customizable box with a snap-on lid, optionally divided into segments, optionally with a sunken or raised label on the base, lid or one of its segments. The corners of the box are rounded (or not ;-)) which I think makes it feel very smooth and comfortable to carry on your person. I find a radius of 5 mm to be quite “round”. You may prefer 3, or 7. It's up to you.

Snap-fit

The parts are made to fit together by a small overlap. Bottom parts have a protruding 'wall' on top, top parts a 'recess' at the  bottom. The recess is a little narrower than the wall. The layered nature of the print provides a rough but satisfying sliding, almost ratcheting experience.
 
The outer dimensions are specified as parameters. The lid and optional segments each have their own height; what's left over is the height of the base. Everything else is also customizable - label, label size, number and size of the segments, etc. 

Customization

The print profile provided is just an example. In this case, it's what I call my “money box”. I recently replaced my wallet with a bank card holder (actually, the great Advanced Lever Action Wallet), which leaves no room for cash. I now keep my cash in this box, so I can choose what to take with me. I then made another of these boxes for the multitude of “other” cards that were in my wallet. See the print profile for the card box.

Segments

The money box consist of three parts. From the bottom up: a base, a middle segment, and a lid. You specify the outer length and width of the box (50 x 15 mm) and the outer height (80mm). Set the lid height to 20 mm, and select one segment of 30 mm. The base will then be 80 - 20 - 30 = 30 mm high. By default, the parts overlap 4 mm internally, and the segments and the lid are just a bit narrower to hold everything together. The segments are even a bit narrower than the lid to facilitate opening the box - the lid will pop off, not one of the segments.

If you set the number of segments to 0, or the the segment height to 0, there will be no segments. just the base and lid. You can even set the lid height to 0 and you'll just get a base. You get the picture - just experiment with the customization and you'll find almost everything self explanatory.

Printing with supports is recommended for the segments. Normal (as opposed to tree) supports can very easily be removed.

Mix colors without AMS

The segments allow you to mix colors without using an AMS - just print each segment in its own color. Also, you can put the label on a small segment so you can change it without having to reprint the whole box. Just make sure to use the same settings for each segment - except the height of course.