Shared trellis

I have a 15 ft section of heavy duty trellis that I attached to a party fence (terrace). My neighbour and I are good friends and he is happy for me to grow climbers on the trellis. Over the past five years or so I have grown Montanta and flowering honeysuckles on it. The whole thing came down in the winter gales.
In fact, neither the clems nor the honeysuckle had proved very successful, for while they did give privacy to the gardens and give good flowers, they created a great mess too. The honeysuckle always has a mass of dead-looking twiggy bits sticking out - really very ugly - and the Montana grew so fast I'd have to prune it back every month on both sides of the fence. It looks awful in winter.
My neighbour is not really a gardener and I don't want to inflict any major upkeep on him (or me). I do want something that does give some kind of screen but is easy(er) to maintain. Climbing roses don't really screen much. Perhaps a calm, evergreen clem? Both are narrow gardens, so I don't really want to put more shrubs in and lose the space.
Any ideas of other climbers? Thanks
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They are evergreen and will twine through a trellis. After a couple of years they will provide gentle, year round screening and beautifully scented flowers in the summer. They won't like it if the soil is too heavy, cold and wet in the winter and they prefer a warmer sheltered spot if possible.
That said - mine survived the Beast from the East last year in clay. (Survived mind you - didn't exactly thrive - but it's growing away again now).