A bedrail clamp with a jaw member positionable by an actuating member, the actuating member being configured to move to move the jaw member away from the bedrail and toward the bedrail to move the jaw member into contact with the bedrail to secure the bedrail against the clamp housing. Either the actuating member or the jaw member features an inclined surface that includes a first portion with a first angle and a second portion with a second angle. Methods of operating a bedrail clamp.