Apparatus and methods are provided for applying ultrasound pulses into tissue or a medium in which the peak negative pressure (P−) of one or more negative half cycle(s) of the ultrasound pulses exceed(s) an intrinsic threshold of the tissue or medium, to directly form a dense bubble cloud in the tissue or medium without shock-scattering. In one embodiment, a microtripsy method of Histotripsy therapy comprises delivering an ultrasound pulse from an ultrasound therapy transducer into tissue, the ultrasound pulse having at least a portion of a peak negative pressure half-cycle that exceeds an intrinsic threshold in the tissue to produce a bubble cloud of at least one bubble in the tissue, and generating a lesion in the tissue with the bubble cloud. The intrinsic threshold can vary depending on the type of tissue to be treated. In some embodiments, the intrinsic threshold in tissue can range from 15-30 MPa.