Coherent optical communications, integrated optics, and interferometric sensors require that single-mode fibers maintain a stable state of polarization. With a broadband source, wavelength averaging of the power in either orthogonally polarized HE 11 mode permits a simple measurement of the power transfer to the cross-polarized state (the h value). Polarization-holding quality was measured on several single-mode fibers with strain birefringence that had been induced by a new preform deformation method or a gas-phase etching technique. The fibers exhibited h values from 2.3 × 10−5 m−1 (average polarization-holding to −24 dB) to 8.9 × 10−4 m−1 with beat lengths (at λ = 632.8 nm) from 1.7 to 10 mm when the power is wavelength averaged over the 800-to 1100-nm range.