We have measured the pressure dependence of the order-disorder transition temperature (T-ODT) in two styrene-isoprene diblock copolymers containing 24 and 48 wt % styrene (M(w) = 20 500 and 16 500 g mol(-1), respectively). Small-angle X-ray scattering measurements indicate that T-ODT rises linearly with increasing hydrostatic pressure in both systems at a rate of +20 degrees C kbar(-1) (approximately) over the range from 0 to 600 bar; deviations from linearity appear at higher pressures. This increase is approximately twice the value that we have previously estimated from measurements of changes in polymer characteristics with high pressure.(1) We present dilatometric measurements across the ODT which show a volume change (Delta V/V) of order +5 x 10(-4) upon disordering. The observation of a change in specific volume at the ODT has implications for experimental and theoretical investigations of polymer phase behavior, which we discuss. Finally, we demonstrate the existence of pressure-induced ("barotropic") phase transitions in these materials and compare their characteristics with those of the analogous temperature-induced ("thermotropic") transitions.