Ink-bleed interference is undesirable as it reduces the legibility and aesthetics of affected documents. We present a novel approach to reduce ink-bleed interference using functional minimization. In particular, we show how to modify the Chan-Vese active contour model to incorporate information from the front and back sides of the ink-bleed document. This contour model is particularly useful as it does not require edge extraction or explicit thresholding of the document. In addition, we show how functional minimization can again be used to restore broken foreground strokes that arise when strong ink-bleed overlaps with foreground strokes. The experimental results show that our functional minimization method produces better results than recent ink-bleed reduction techniques. To provide a complete framework, we also show how simple user assistance can be further exploited to improve the results.