Polymer particles or beads for use as opacifiers in paints are described in which a core is provided with a hard sheath and the particle has one or more voids produced by reaction with a nonvolatile permanent or fixed base. The sheath is a copolymer of an ethylenically unsaturated aliphatic monomer free of acid groups and at least 2 percent by weight of a soft ester-containing monomer and optionally styrene in an amount of up to 25 mole percent. The core is formed from an ethylenically unsaturated monomer with acid functionality.The sheath polymer has a glass transition temperature of at least 40.degree. C. The particles have a size of up to 40000 nanometers before swelling the core by some 150 to 2000 percent.