As far as removing the weeds, I can't speak to how to eradicate them per se. But in my beds I try to keep a layer of mulch down on everything and while you will likely never be free of weeds the mulch certainly keeps things considerably more under control. I can tell you that with vinca if you encourage it to grow and the plants are close enough together eventually they should form a mat that prevents weeds from getting a good foothold.

Kate

Thanks, I'll try adding more mulch. Already have some, but probably not enough.

How about grass coming up through a thick mat of ground cover (don't remember what it is. Can a systemic grass killer be brushed on the top of the grass springs and knock it out? I've never used any kind of chemical killer, but can't really even get to the grass roots to pull them.

If you are very careful you can brush the grass with roundup...but be very careful not to get any on the vinca.
The way I keep weeds down in a new bed of ground cover is with mulch and Preen.
Linda C

This happens with my vinca, especially in the areas that are not densely established. I put on rubber gloves, cover them with fabric gloves. Dip fingers in Round Up to soak the fabric. Now I can touch or massage the Round Up onto the weed foliage without touching the vinca. Make sure your skin doesn't come in contact with the Round Up!

good luck!