An openable covering construction for pergolas and verandas, characterized in that said openable covering construction comprise a plurality of adjoining and partially overlapping bands longitudinally mounted on a supporting frame by a driving system allowing each said bands to be rotated about a longitudinal axis thereof parallel to a sloping side of said covering construction, said driving system driving said bands to at least two positions, a closed position, thereat said bands are partially overlapped onto one another and substantially parallel to the covering construction plane, and an opened position thereat each said band is rotated to a substantially vertical condition with respect to said covering plane, each said band comprising a section member including a contoured surface including, at a side thereof, a perpendicular side wall and, at an opposite side thereof, a channel defining curved wall, thereby a surface directly exposed to rain of said covering construction forms a water collecting and disposal of channel.