Layered materials containing hydrocarbon bilayers capable of transitioning between an ordered and partially disordered state can exhibit large temperature and entropy changes─termed barocaloric effects─in response to a change in hydrostatic pressure. These barocaloric materials can, in principle, be used to drive heating and cooling cycles with higher efficiency and less environmental impact than conventional fluorocarbon refrigerants. However, much remains to be understood about how to manipulate the thermodynamics and kinetics of hydrocarbon order-disorder, or "chain-melting", transitions in the solid state in order to design materials with properties tailored for specific thermal applications. Here, we report a chain desymmetrization strategy to modulate the phase-change behavior of a new family of asymmetric dialkylammonium halide salts. In particular, we demonstrate that chain desymmetrization can lead to reduced phase-change thermal hysteresis while maintaining large entropy changes. This translates to a significant reduction in the pressure required to reversibly drive nonzero entropy changes, with asymmetric dialkylammonium salts able to access reversible entropy changes at pressures nearly 80% lower than their symmetric counterparts. This work expands the scope of chain-melting materials that exhibit strong barocaloric effects and offers insights into the factors that influence the reversibility of barocaloric materials.