I finally found containers I like for storing mini ink cubes. They don't have lids, but stacking an empty box on top creates a lid of sorts; for me they'd be more for home use.
They're stackable: a large box on top of a large, two smalls on top of a large, or a small on a small. A box nests into the box below it about an inch, so these are very stable even if you stack them high. The plastic feels substantial - not a hard more brittle plastic, but not flimsy - just a bit of give at the sides.
For Alexites, you can stack four high in a deeper Alex drawer, and sorta kinda three high in a shallow drawer - sort of because there's a tiny bit of a catch on the box edge. ETA: three worked in one shallow drawer but not another. And a large plus a Tim tin fit side by side in a drawer if you put them in the long way.
LARGE holds 35 minis - 7 rows of 5. I checked Versafine, Hero Arts, Color Theory and Altenew. Distress cubes are a different story. They're minutely larger (!) so easily go 7 across, but 4 down, unless you don't mind them squashed next to each other and grumbling.
SMALL holds 15 minis or 12 Distress.
These could work for tons of other items too. I don't like large hinged boxes because when open, the lids have to be accommodated, doubling the size of the box. I don't mind Tim's tins because they're small. (Jennifer McGuire lined a drawer with Tim tins and took the lids off.)
The Container Store lists them by SKU number,
not by name, which is "livinbox shallow drawer organizer." No "g" in livin.
Large box $3.99, SKU 10069218, 7-1/8" x 10-1/4" x 1-13/16" highSmall box $3.49, SKU 10069217, 7-18" x 5-1/8" x 1-13/16" high
There's also a narrow box. A Container Store employee helped me, and when she saw the minis I brought, excitedly asked if I made cards, since a friend of hers does for every holiday and "they're beautiful!" : )
http://www.containerstore.com/s/clea...583&q=10069217
I didn't think a photo would be that helpful, but if anyone wants one, let me know. I've had one of the small boxes for ages, and it finally dawned on me after I looked at tons of other possibilities that it might do the trick.
Egads, sorry this is so long. I wanted to include everything I could think of in case someone who doesn't live near a Container Store is interested.