A low cost composition that cures rapidly and which is suitable for coating an optical fiber comprises at least one ethylenically unsaturated monomer; at least one photoinitiator; and at least one non-radiation-curable polar polymer having pendent groups that facilitate low energy chemical bonding, hydrogen bonding, dipolar interactions or other interactions with radical compounds formed during polymerization of the monomer. The non-radiation-curable polar polymer(s) are inexpensive and reduce and/or eliminate the need for expensive urethane acrylate oligomers, without sacrificing properties, and while achieving rapid cure speeds.