Accurate estimation of the body surface area (BSA) involved by a rash, such as psoriasis, is critical for assessing rash severity, selecting an initial treatment regimen, and following clinical treatment response. Attempts at segmentation of inflammatory skin disease such as psoriasis perform markedly worse on darker skin tones, potentially impeding equitable care. We assembled a psoriasis dataset sourced from six public atlases, annotated for Fitzpatrick skin type, and added detailed segmentation masks for every image. Reference models based on U-Net, ResU-Net, and SETR-small are trained without tone information. On the tuning split we sweep decision thresholds and select (i) global optima and (ii) per Fitzpatrick skin tone optima for Dice and binary IoU. Adapting Fitzpatrick specific thresholds lifted segmentation performance for the darkest subgroup (Fitz VI) by up to +31 % bIoU and +24 % Dice on UNet, with consistent, though smaller, gains in the same direction for ResU-Net (+25 % bIoU, +18 % Dice) and SETR-small (+17 % bIoU, +11 % Dice). Because Fitzpatrick skin tone classifiers trained on Fitzpatrick-17k now exceed 95 % accuracy, the cost of skin tone labeling required for this technique has fallen dramatically. Fitzpatrick thresholding is simple, model-agnostic, requires no architectural changes, no re-training, and is virtually cost free. We demonstrate the inclusion of Fitzpatrick thresholding as a potential future fairness baseline.