While ascending in the plumbing system of volcanoes, magma undergoes decompression at rates spanning several orders of magnitude and set by a number of factors internal and external to the volcano. Slow decompression generally results in an effusive or mildly explosive expansion of the magma, but counterexamples of sudden switches from effusive to explosive eruptive behavior have been documented at various volcanoes worldwide. The mechanisms involved in this behavior are currently debated, in particular for basaltic magmas. Here, we explore the interplay between decompression rate and vesiculation vigor by decompressing a magma analogue obtained by dissolving pine resin into acetone in varying proportions. Analogue experiments allow direct observations of the processes of bubble nucleation and growth, flow dynamics, and fragmentation that is not currently possible with magmatic systems. Our mixtures contain solid particles, and upon decompression, nucleation of acetone bubbles is observed. We find that mixtures with a high acetone content, containing smaller and fewer solid particles, experience strong supersaturation and fragment under very slow decompressions, despite having low viscosity, while mixtures with lower acetone content, with more and larger solid particles, degas efficiently without fragmentation. We interpret our results in terms of delayed bubble nucleation due to a lack of efficient nucleation sites. We discuss how a similar mechanism might induce violent, explosive expansion in volatile-rich and poorly crystalline low-silica magmas, by analogy with the behavior of rhyolitic magmas.