Centaurea montana, which you already have, is invasive both with runners and seeds.

Sounds like you want groundcovers

If soil is moist or mulched try golden creeping jenny or vinca minor (various colors of flowers available & even variegated foilage types). If you tend the spot regularly & remove the runners you can enjoy the burgundy or variegated foliage of creeping carpet bugle or Ajuga. It sends runners in spring through summer, so needs tending or will overrun into other plants. With care & moisture it's a tough plant that doesn't mind being stepped on some.

If soil is more dry you could try any of the thymes plus you can harvest the culinary types.

Have you tried London Pride, Saxifraga x urbium? There are several Saxifragas that are low growing.

Have you tried sedums or sempervivium? There are numerous low growers to select from.

Go to your local independent nursery and ask them to show you the groundcover section. Have your list handy & you should find at least one or several plants that fit your requirements. They should know what is hardy in your zone as well & have those plants available if not sold out for the season.

weislaw, it doesn't set seed here, & it's failing in the drought. I was already considering replacing it (with a tallish NOID chrysanthemum in dark red).

Maybe I should explain this bed, as it's a bit different. it's only 3 ft wide by 17 ft long, between two paved driveways, on a slope. I dealt with the slope by making it a raised bed. Yes, it is a bit on the dry side. The idea is "jewelbox", like a miniature cottage garden. Please don't take it personally if I don't find your suggestions suitable, it's just such an odd & specific garden. Also, I'm trying to avoid having "more of what everyone else has"

corrine1.. no on ajuga. "drifts" just don't work in this space. I do use some groundcovers, the more civilized ones. Here periwinkle will eat an entire garden in one bite. :-)

I already use houseleek ("Firebird") & creeping thyme ("Pink Chintz") at the most exposed end of the bed. I'll look at which saxifrages are available here.

How about dwarf daylilies in an interesting variety so your entranceway looks different and special? Many colors available. Maybe very small dwarf zinnias to fill in, in front and between, until the daylilies get lush, dwarf zinnias in shades to contrast with daylily color. Buy plants so you can see sizes together, harvest your zinnia seed so you get the right height and color in the future. Dwarf modern daylilies that rebloom and rebloom. I grow old fashion daylilies so I cannot be of help with variety.

Divide daylilies every other year; fill in empty areas to create lush look then forget about zinnias. Later divisions of daylilies can be used as front of the border plants in other areas to create a coordinated look to your garden. Attract butterflies to your front door and your guests will be impressed. If you hate the idea, that's fine, no prob!

You've given me some ideas, folks. Thanks.