Minimally invasive surgeries, such as cardiac ablations, increasingly resort to magnetically-steered catheters. To enhance the dexterity and tissue interaction capabilities of these devices, researchers have developed catheters with variable stiffness (VS). These devices can transition from a soft to a rigid state, or vice versa, on command by means of thermal or pressure triggers. However, the stiffness change of existing devices is either too slow (thermal-triggered) or too low and limited to only two states that prevent continuous stiffness change (pressure-triggered). Here, we propose a method for addressing the two aforementioned limitations of pressuretriggered devices. Firstly, we describe a control method for rapid and continuous stiffness change based on fiber jamming (FJ). This method allows for smooth stiffness adjustment of the catheter across more than 100 steps by regulating vacuum pressure, which affects friction force between the fibers. Secondly, we assess important design parameters of the proposed catheter, such as fiber material and roughness, to identify optimal values that increase the stiffness range up to 46%. This enables the new FJ catheter to be as safe as clinical magnetic catheters in the soft state while navigating through the body and rapidly become stiff as conventional manual catheters to achieve comparable forces onto the heart tissue.