Sort items in Item Showcase?

It looks like the items in my item showcase are sorted according to the order in which they were added to the block. I realize that I can drag them around in the list, but is there a way to have them automatically sort by some field, say, title?

TIA.

The attachment blocks are designed to show the attached items in the specific order the user selects, so it’s just the drag-and-drop option.

Modules can add their own blocks, and a block could be written that takes an option for how to sort the attached items and essentially ignore the user-selected drag-drop order.

Also, the browse preview block does allow you to specify sorting, in the same way that it can be specified for a regular browse page, but the display of items is obviously different from the showcase block.