SURF contrast imaging, as described previously in the literature, is a contrast agent detection technique achieved by processing of the received signals from transmitted dual frequency band pulse complexes with overlapping high-frequency (HF) and low-frequency (LF) pulses. The transmitted HF pulses are used for image reconstruction, whereas the transmitted LF pulses are used to manipulate the scattering properties of the contrast agent. As with harmonic contrast agent detection techniques, nonlinear wave propagation will, in most situations, also limit the specificity with the SURF contrast technique when transmitting overlapping HF and LF pulses. The present paper proposes an alternative SURF contrast imaging technique using transmit dual frequency band pulse complexes with non-overlapping HF and LF pulses. If the frequency of the LF manipulation pulse is close to the bubble resonance frequency, numerical simulations indicate a significant ring-down effect of the LF bubble radius response. Utilizing this bubble ring-down effect and transmitting the HF pulse just after the LF pulse, a contrast agent specificity approaching infinity accompanied by a contrast agent sensitivity only for contrast bubbles having resonance frequencies within a narrow frequency range may be obtained.