A water-soluble terpolymer consists essentially of the polymerization product of the following monomers : (a) (meth)acrylamide, (b) an ethylenically unsaturated, aliphatic carboxylic acid or a salt thereof, and (c) a water-soluble, polyvinyl monomer, wherein (c) comprises <0.07 mole % based on total monomers; a 1% solution of the terpolymer is capable of passing through a 200 mesh screen substantially without retention of polymer solids, and the terpolymer has a reduced specific viscosity of about 3.0 deciliters/g or less. The process for preparing the polymer includes the step of continuously adding both components of a redox initiator. The terpolymer is useful as a dry strength additive for paper.