The disclosure describes devices and methods for asymmetrical irradiation at a body cavity or site, such as after removal of tissue, e.g. biopsy or cancer. One device includes a lumen which is off-set or off-settable from a longitudinal axis to increase the intensity of radiation received from a radiation source by a first tissue portion surrounding the body cavity and to reduce or minimize radiation received by a second tissue portion (e.g. healthy tissue) surrounding the body cavity.