Which convulvulus, Keeny? There are lots of varieties from neat annuals for ground cover (such as C.minor) to the shrubby perennial C.cneorum.
I'm assuming that you're not thinking of planting C.arvensis which is the 'dreaded' bindweed!

If one is going to be really pedantic, the great big Bindweed of hedges in Calystegia sepium. Convolvulus arvensis is smaller and more likely to be found in grassland than hedges.
Not that anyone would want to plant either of them.

Have you got is full name Keeny? As Urbanite says, can't help you without knowing which one it is.