Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that far from being fibre bundles. Murray and Stevenson proved on simply-connected manifolds, bundles with connected fibres, always have a torsion $DD$-class. In this note I prove an analogous result for wide class of principal bundles, relaxing the requirements fundamen...

We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P5. In characteristic p, we obtain rank two bundles on P4 and rank three bundles on P5. In arbitrary characteristic, we obtain rank three bundles on P4 and rank two bundles on the quadric S5 in P6.