A suitable modification of the cylinder kernel of the dual topological unitarisation scheme is suggested, to solve the main shortcomings of DTU: the pomeron-f identity and the ω problem. To account for the overlapping clusters appearing in unitarity equations, a glueball kernel is added to the normal twisted-loop kernel. Separate pomeron, f and f′ reggeons are obtained, the parameters of which agree well with present phenomenology. A good description of the ω and φ exchanges is also possible. The corresponding glueball singularities lie at j ∼ 0.6 (lower than the often suggested value j ∼ 1.0) and at j ∼ 0.1. In both cases, the strength of the glueball kernel is smaller than the strength of the twisted-loop kernel.