The present invention is of a system and method for accurate cryoablation, useable to enhance a surgeon's ability to accurately cryoablate a selected cryoablation target and to limit cryoablation to that selected target. Presented are apparatus and method for accurately delimiting a cryoablation volume, for minimizing damage to tissues surrounding a cryoablation volume, and for real-time visualization of a border of a cryoablation volume during cryoablation. Also presented are a method for mildly heating tissues during cryoablation, cryoprobes operable to simultaneously cool first tissues while heating second tissues, and cryoprobes operable to cool tissues extending in a first lateral direction from those probes while not substantially cooling tissues extending in a second lateral direction from those probes.