Looking for ideas... low growing perennials

I'm looking for some ideas for low growing perennials that I can plant around the base of my roses. At the moment I have lots of forget-me-not (FMN) growing around them and that's fine, except they die off... I'd like something a little more permanent along the same lines. I have lots of perennials around but I particularly like the way the FMNs grow densley and not too tall. Penestemon are too tall for most roses though I have lots of them as space fillers. Needs to be able to cope with a dry summer and freezing in winter. The roses with the FMN under them always do better than the ones without so I'd like something shallow rooted that can grow right in and around the rose trunks. I have grown lambs ears around them before and don't like the way they die off. I have tried seaside daisies but they grow up the trunk and get too high... thinking I might try Snow in Summer and see how that goes. Would like it to spread by runners or by division. I have chamomile too and really like this option. Yarrow gets too high in a rich garden bed but is also nice.

Catmint!!! That would be good. What about livingstone daisies? Are they annuals? The FMN self seed all over the place and come up like weeds (I pull them out like weeds too )... a perennial FMN would be good

Dee... does your snow in summer-like plant have yellow flowers instead of white? there is one like this around that also looks really nice but I don't know what it is.

What about violets? They are hard to get rid of once you have them though and my chooks love them

Isn't Alyssum an annual? I have prostrate clematis, penstemon, geranium, potentilla, a prostrate mint bush, a prostrate ceanothus, aquilegia, alstromera, daisies, crocosima, dierama, bearded and Dutch iris, lemon balm, chamomile, lupins, peony (tree and bush), carnations, lavender, sisyrinchium (yellow, blue, and white - these are really nice... I have one called 'Devon Skies' that I'm going to put around as many roses as I can) and a few others through the gardens now... but am looking for a perennial that spreads by layering/runners/stolons etc that will form a dense weed excluding buffer around the rose trunks... I'll take a photo tomorrow of the forget-me-nots around the roses to explain what I mean. I have a lot of cuttings in of a dwarf pink lavender called 'Fairy Floss' that gets to about 30cm tall that I'd like to put around but again... it doesn't spread and run.

Keep the ideas coming

Was thinking of Thyme too... anyone use this?

They self seed well enough but they seem to peak and then die off allowing plenty of time for other adventitious weeds to jump in.

Yeah... I was thinking of Ajuga too... I have a lot of it here in along a path... I don't know that I would bother pulling it out from around the rose as this is the effect I am trying to achieve... cover right up to the trunk and believe roses (at least here because the soil is very friable and deep) can cope with crowding with shallow rooted groundcovers. I was looking at campanula in the GE cat. that arrived yesterday too thinking it looked pretty good for what I want as well... hmmm

This is the forget-me-nots around 'Mary Rose' and 'Maurice Utrillo' (note all the new growth on 'Mary Rose' already... think I'm going to shorten the left a bit to even her up but she's even got a flower on her atm)... sorry about the poor pic... was taken with the point and shoot pretty much in the dark. The grassy looking plant infront of the FMN is the sisyrinchium.