We revisit an alternate explanation for the turbulent nature of molecular clouds - namely, that velocity dispersions matching classical predictions of driven turbulence can be generated by the passage of clumpy material through a shock. While previous work suggested this mechanism can reproduce the observed Larson relation between velocity dispersion and size scale ($sigma propto L^{Gamma}$ with $Gamma approx 0.5$), the effects of self-gravity and magnetic fields were not considered. We run a series of smoothed particle magnetohydrodynamics experiments, passing clumpy gas through a shock in the presence of a combination of self-gravity and magnetic fields. We find powerlaw relations between $sigma$ and $L$ throughout, with indices ranging from $Gamma=0.3-1.2$. These results are relatively insensitive to the strength and geometry of magnetic fields, provided that the shock is relatively strong. $Gamma$ is strongly sensitive to the angle between the gas bulk velocity and the shock front, and the shock strength (compared to the gravitational boundness of the pre-shock gas). If the origin of the $sigma-L$ relation is in clumpy shocks, deviations from the standard Larson relation constrain the strength and behaviour of shocks in spiral galaxies.
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