Described herein are partitioning devices for reducing ventricular volume that may be secured within a ventricle and separate it into a productive portion and a non-productive portion. The partitioning devices described herein may include a reinforced membrane and may be secured within the heart chamber by sealing them to the wall of the heart chamber, for example, by inflating an inflatable element on the periphery of the device. All or a region of the non-productive portion formed by these devices may be enclosed within a container or bag. The non-productive portion may be filled with a material, including occlusive materials (e.g., vasoclusive coils). Sealing and/or filling the non-productive portion formed by the devices described herein may help prevent leakage from the non-productive region. Also described herein are systems including these devices and methods of using them, which may be suitable for treating patients with heart disease, particularly congestive heart failure.