Next-generation radio interferometric telescopes will exhibit non-coplanar baseline configurations and wide field-of-views, inducing a w-modulation of the sky image, which induces the spread spectrum effect. We revisit the impact of this effect on imaging quality and study a new algorithmic strategy to deal with the associated operator. In previous studies it has been shown that image recovery in the framework of compressed sensing is improved due to this effect, where the w-modulation can increase the incoherence between measurement and sparsifying signal representations. For the purpose of computational efficiency, idealised experiments with a constant baseline component w were performed. We extend this analysis to the more realistic setting where the w-component varies for each visibility measurement. Firstly, incorporating varying w-components into imaging algorithms is a computational demanding task. We propose a variant of the w-projection algorithm, which is based on an adaptive sparsification procedure, and incorporate it in compressed sensing imaging methods. Secondly, we show that for varying w-components, reconstruction quality is significantly improved compared to no w-modulation, reaching levels comparable to a constant, maximal w-component. This finding confirms that one may seek to optimise future telescope configurations to promote large w-components, thus enhancing the fidelity of image reconstruction.