We present neutron-scattering measurements of Bose-Einstein condensation, the atomic momentum distribution, and final-state effects in liquid He-4 under pressure. The condensate fraction at low temperature is found to decrease from n(0) = 7.25 +/- 0.75% at saturated vapor pressure (p similar or equal to 0) to n(0) = 3.2 +/- 0.75% at pressure p = 24 bar. This indicates an n(0) = 3.0% in the liquid at the liquid/solid coexistence line (p = 25.3 bar). The atomic momentum distribution n(k) has high occupation of low-k states and differs significantly from a Gaussian [e. g., a classical n(k)]. Both n(k) and the final-state function broaden with increasing pressure, reflecting the increased localization of the He-4 in space under increased pressure.