Improved medical suturing devices, systems, and methods may hold a suture needle at a fixed location relative to a handle of the device, allowing the surgeon to grasp and manipulate the handle of the suturing device to insert the needle through tissues in a manner analogous to use of a standard needle gripper. Cycling the handle from a closed position to an open position and back to the closed position may alternate the device between gripping the needle with a first clamp (for example, along a proximal portion of the needle) to gripping the needle with a second clamp (for example, along a distal portion of the needle) and optionally back to gripping with the first clamp, with the needle often staying at a substantially fixed location relative to the suturing device body. Related single-clamp needle grasping devices can be bent plastically by a surgeon, and/or have bodies that are grasped by a hand while a portion of the hand actuates a handle.