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Soliton-based supercontinuum generation is a powerful approach for generating light with the desired properties, although limited dispersion tuning capabilities remain a key challenge. Here, we introduce liquid-core fibers (LCFs) with longitudinally controlled dispersion of a higher-order mode, achieved by axial modulation of the liquid core diameter. This approach provides a versatile photonic platform with unique dispersion control capabilities that are particularly relevant to ultrafast, non-linear frequency conversion. Our tuning concept uses LCFs with anomalous dispersion at telecommunication wavelengths (TE01-mode) and relies on the strong dependence of dispersion on the core diameter. Non-monotonic, complex dispersion profiles feature multiple dispersive waves formation when launching ultrashort pulses. For example, this effect has been used to fill spectral gaps in fibers with linearly decreasing core diameter in order to spectrally smooth the output spectra. Our results highlight the potential of LCFs for controlling dispersion, particularly along the fiber axis, thus yielding novel dispersion landscapes that can reveal unexplored nonlinear dynamics and generate tailored broadband spectra.