Cu-63-NMR experiments of Knight shift and relaxation time T-1 have been per
formed on the two-leg spin ladders of a Sr2Ca12Cu24O41 single crystal at se
veral pressures up to the critical pressure P-c for the stabilization of a
superconducting ground state. The data confirm the onset of low-lying spin
excitations at P-c observed previously [Science 279, 345 (1998)] and reveal
a marked decrease of the spin gap under pressures above 20 kbar although a
significant fr action of the spin excitations remains gapped at P-c = 32 k
bar. A comparison between NMR and transport data under pressure suggests th
at the depression of the spin gap can be ascribed to an increase in the int
erladder exchange coupling, possibly mediated by the ladder-chain interacti
on along the b-direction.