Convolvulus can be an ornamental plant. There is a reason it is called MORNING Glory.  It's why people plant it.  It's commonly sold in nurseries.  There's a large purple flowered variety that is growing throughout my Ventura city neighborhood.  It's quite charming highlighting the orange fruit high in the canopies of citrus and along backyard fences.  There are also pink stripped varieties.  They also seem to grow well, and when you decide it's time that they had taken over too much of the garden, it's really hard to get rid of them  The seeds are everywhere and they lie dormant, ready to emerge to recolonize that orange tree you had just cleaned out. 

Listen to Weedologist Lynn Sosnoskie's advise on how to deal with this beautiful menace in the orchards.  This podcast  is prepared by Phoebe Gordon of UC's "Growing the Valley".