Histotripsy produces non-thermal lesions by generating, when an intrinsic threshold is exceeded, dense highly confined energetic bubble clouds that mechanically fractionate tissue. This nonlinear thresholding phenomenon has useful consequences. If only the tip of the waveform (P-) exceeds the intrinsic threshold, small lesions less than the diffraction limit can be generated. Moreover, side lobes from distorting aberrations can be “thresholded-out” wherein part of the relatively undistorted main lobe exceeds the intrinsic threshold producing a clean bubble cloud (and lesion) conferring significant immunity to aberrations. The short very high intensity histrotripsy pulse is significantly backscattered by the cloud it creates, allowing aberration corrections to be made in real time using transmitting elements as receivers. This allows significant increases in peak negative pressures that can be generated through the skull. These same backscattered signals allow a 3D representation of the bubble cloud to be generated providing excellent noninvasive bubble cloud localization. These refinements allow noninvasive transcranial procedures outside of expensive MRI machines.