The cononsolvency effect on the swelling of different stimuli-sensitive microgels was investigated in water/methanol mixtures. Poly(N,N-diethylacrylamide) (PDEAAM) and poly(N-isopropylacrylamide) (PNIPAM) homopolymer microgels, a PDEAAM-core-PNIPAM-shell microgel, and a poly(N,N-diethylacrylamide-co-N-isopropylacrylamide) (P(DEAAM NIPAM)) microgel have been synthesized. The core-shell and the copolymer microgel have similar compositions; the PDEAAM core of the PDEAAM-core PNIPAM-shell particle contributes 80% to the total mass, and the copolymer consists of 75% DEAAM and 25% PNIPAM. They were characterized with dynamic light scattering (DLS) and small-angle neutron scattering (SANS). Microgels containing PNIPAM show the cononsolvency effect, and the particle size reaches a minimum at a methanol fraction of x(methanol) = 0.2. Moreover, in core-shell microgels, the cononsolvency effect can be limited to one compartment of the particle. A core-shell microgel with a PDEAAM core and PNIPAM shell reveals a sharp surface at x(methanol) = 0.2; i.e., the PNIPAM shell is collapsed, and the PDEAAM core is swollen in the solvent mixture. The results demonstrate how responsive swelling properties of such polymers in solvent mixtures can be tuned via microgel morphology. Core-shell microgels provide new opportunities for encapsulation of guest molecules.