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Linear polarization measurements at milliarcsecond resolution have been made at λ6 cm using four stations of the U. S. VLBI Network and the Mark III recording system. Calibration of the cross-polarization contamination of the feeds was done using the cross- to parallel-hand fringe ratios of the essentially unpolarized source 0Q 208, and is believed accurate to 0.5%. Other sources, such as AO 0235+164 and 0106+013, which are nearly unresolved in the unpolarized fringes, show clear signs of resolution in their polarized fringes. A preliminary map of the BL Lacertae object OJ 287 is compatible with a weakly-polarized optically-thick core and a highly-polarized optically-thin jet about 5 mas in length.