A study of the phase and amplitude sensitivity of the recently proposed Renyi time-frequency information measure leads to the introduction of a new "Jensen-like" divergence measure. While this quantity promises to be a useful indicator of the distance between two time-frequency distributions, it is limited to the analysis of positive definite TFDs. In spite of this rather severe limitation, this measure could prove useful for time-frequency based detection. We illustrate with an example of detecting a signal in additive noise.