Pressure-release melting of the earth's mantle is thought to be an isentropic process. The intersection of an isentropic melting path with a solid-state phase transition affecting the residual minerals must result in some change in melting rate unless the entropy of reaction of the phase transition is exactly zero. Furthermore, both phase transitions of primary interest for peridotite melting in the upper mantle (garnet-spinel peridotite and spinel-plagioclase peridotite) have positive Clapeyron slopes, and hence the lower-pressure assemblage has a higher molar entropy. Thus, these phase transitions must retard isentropic, decompression melting, or even lead to freezing. There cannot be enhanced melting accompanying such phase transitions, even if there is a cusp in the solidus. Model calculations in simple one-component and two-component systems demonstrate the effect of solid-solid phase transformations on isentropic decompression melting. Conversion of low entropy solids to high entropy solids in the presence of liquid results in crystallization; the amount of crystallization depends on the relative molar entropies of the solid and liquid phases, on the modal abundance of the reacting solid phases, and on the proportion of liquid present when the reaction is initiated. The effect of solid-solid phase transitions on freezing is more pronounced for fractional fusion than for batch fusion in that melting ceases for a finite pressure interval at pressures below the invariant point where melt and the solids involved in the phase transition coexist. Isentropic upwelling calculations for a model nine-component peridotite using a modified version of the MELTS potential minimization algorithm (Ghiorso et al., 1994; Ghiorso and Sack, 1995) verify that the simple-system behavior can be extended to multicomponent, mantle-like systems: melt production is suppressed during the transformation from garnet to spinel peridotite and for batch melting there is freezing during the transformation from spinel to plagioclase peridotite; these effects are exaggerated during fractional fusion and barren zones are produced as in the simple systems. These results imply that melt production during upwelling may be highly nonuniform. Very slow melt production in the spinel-garnet transition region may enhance development of UTh disequilibria. If significant contributions of melt from garnet peridotite are needed to account for the Lu-Hf systematics and REE patterns in MORB, melting must begin deep within the garnet stability zone. If plagioclase ever appears in the melting residue, this event is likely to end decompression melting despite further upwelling. Regions such as the garnet-spinel and spinel-plagioclase peridotite transitions may serve as nucleation sites for solitary waves in porous flow or regions of fracture formation and enhanced melt segregation.