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We have in earlier papers presented an extension of Mueller's dipole cascademodel, which includes sub-leading effects from energy conservation and runningcoupling as well as colour suppressed saturation effects from pomeron loops viaa ``dipole swing''. The model was applied to describe the total and diffractivecross sections in $pp$ and $\gamma^*p$ collisions, and also the elastic crosssection in $pp$ scattering.  In this paper we extend the model to describe the corresponding quasi-elasticcross sections in $\gamma^*p$, namely the exclusive production of vector mesonsand deeply virtual compton scattering. Also for these reactions we find a goodagrement with measured cross sections. In addition we obtain a reasonabledescription of the $t$-dependence of the elastic $pp$ and quasi-elastic$\gamma^\star p$ cross sections.

Elastic and quasi-elastic $pp$ and $\gamma^\star p$ scattering in the Dipole Model