We report on an investigation of the structural relationship between the core and shell components in stimuli-sensitive core/shell microgels. Photon correlation spectroscopy measurements indicate that the presence of the shell alters the extent of core swelling. Core particles composed of poly(N-isopropylacrylamide-co-acrylic acid) (pNIPAm-co-AAc) undergo volume changes as a function of temperature and pH, where deprotonation of the acidic sites results in a volume increase (particle swelling). The addition of a poly(N-isopropylacrylamide) (pNIPAm) shell restricts the core from swelling to its native volume both above and below the pK(a) of acrylic acid. Furthermore, the pH responsive core undergoes only small temperature-induced volume changes above the characteristic lower critical solution temperature (LCST) of pNIPAm (31 degreesC) at pH values where the acid groups are fully deprotonated. The addition of a pNIPAm shell results in compression of the core and induces a large volume change at the pNIPAm LCST. These effects are dependent on the degree of cross-linking in the core and shell. Particles synthesized with lower concentrations of NN-methylenebis(acrylamide) display greater degrees of shell-restricted swelling and compression upon the addition of a pNIPAm shell with an identical cross-linker concentration. These results are interpreted in terms of a previously proposed radial cross-linker density gradient, which places topological restraints upon the core following shell addition.