A convex ostomy barrier assembly for attaching an ostomy appliance to a peristomal skin surrounding a stoma includes a skin barrier, an inlet opening defined in the skin barrier for receiving the stoma, and a convexity adjusting device. The convexity adjusting device includes a convex insert and an inflatable bladder, wherein the convex insert is configured to provide a convexity to the skin barrier and the inflatable bladder is configured to adjust at least one characteristic of the convexity.