We obtain new results for consistent braneworld Kaluza–Klein reductions, showing how we can derive four-dimensional N = 2 gauged supergravity as an exact embedding in five-dimensional N = 4 gauged supergravity. Similarly, we obtain five-dimensional N = 2 gauged supergravity as a consistent Kaluza–Klein reduction from six-dimensional N = 4 gauged supergravity. These embeddings can be lifted to type IIB and massive type IIA supergravity respectively. The new AdS braneworld Kaluza–Klein reductions are generalisations of earlier results on braneworld reductions to ungauged supergravities. The lower-dimensional cosmological constant in our AdS braneworld reductions is an adjustable parameter, and so it can be chosen to be small enough to be phenomenologically realistic, even if the higher-dimensional one is of Planck scale. We also discuss analytic continuations to give a de Sitter gauged supergravity in four dimensions as a braneworld Kaluza–Klein reduction. We find that there are two distinct routes that lead to the same four-dimensional theory. In one, we start from a five-dimensional de Sitter supergravity, which itself arises from a Kaluza–Klein reduction of type IIB* supergravity on the hyperbolic 5-sphere. In the other, we start from AdS gauged supergravity in five dimensions, with an analytic continuation of the two 2-form potentials, and embed the four-dimensional de Sitter supergravity in that. The five-dimensional theory itself comes from an O(4, 3)/O(3, 2) reduction of Hull's type IIB₇₊₃ supergravity in ten dimensions.