Magnetization vs. applied field measurements ( -loops) were taken on YBCO thin films with filaments patterned into them. The YBCO was deposited onto LaAlO 3 substrates using PLD, and the filaments were formed by laser ablation.-loops were taken at 4.2 K in fields up to 9 T using a vibrating sample magnetometer technique, the field applied perpendicular to the film width, . The losses were seen to be greatly reduced by filament width reductions following the standard expression 10. The penetration field was also well described by the standard "high field" expression = (0 4 ) ln( + 1), where is the film thickness. The regimes of applicability of the loss expression were investigated, in particular near . A more general form of the loss equation was obtained and compared with the high-field approximation. The result was that although still increased in proportion to , the rate of increase decreased as approached .Index Terms-AC loss, hysteretic loss, penetration field, YBCO.