Contrast agent destruction transmissions have reduced biological effect in medical diagnostic ultrasound. Ramping-up amplitude and/or ramping-down frequency reduce biological effect. The amplitude ramps up linearly or non-linearly. The change in amplitude or frequency occurs over a single waveform or over a sequence of separate transmissions. An envelope of the single waveform or the sequence of separate transmissions has a non-uniform, asymmetrical, symmetrical, rectangular or other shape. For example, the frequency ramp-down is provided with a non-Gaussian envelope. The amplitude ramp-up or frequency ramp-down is a progressively increasing destructive characteristic or ability, destroying contrast agent at different regions relative to focal regions with a minimum of acoustic energy.